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List of numerical analysis topics

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Generalized quaternion interpolation — generalizes slerp for interpolation between more than two quaternions
1565: 1372: 1324: 926: 503: 329: 108: 6141:— generalization of the Delaunay triangulation that forces certain required segments into the triangulation 3383: 1876: 6620: 6605: 6594: 6508: 6422: 6222: 6144: 6132: 5899: 5878: 5873: 5782: 5777: 5668: 5594: 5084: 5032: 5020: 4822: 4305: 4097: 4047: 3996: 3773: 3768: 3749: 3714: 3652: 3139: 2707: 2572: 2479: 2229: 2107: 1808: 1719: 1597: 1575: 1560: 1530: 1361: 1073: 1068: 776: 737: 573: 545: 527: 445: 309:— represent every number by two floating-point numbers guaranteed to have the unknown number between them 208: 5600: 5562:— solution in the finite-element space is an almost best approximation in that space of the true solution 3611: 3533: 145:— measuring the expected performance of algorithms under slight random perturbations of worst-case inputs 6945: 6785: 6764: 6703: 6687: 6329: 6156: 6126: 6067: 5951: 5925: 5883: 5606: 5430: 5078: 4876: 4654: 4299: 4236: 4154: 4072: 4035: 3899: 3762: 3698: 3646: 3246: 3221: 3108: 3087: 3075: 2968: 2858: 2844: 2802: 2586: 2511: 2155: 1958: 1592: 1570: 1502: 1159: 696: 94: 80: 6242:— standard way of dividing arbitrary convex polygons into triangles, or the higher-dimensional analogue 5325:— two-dimensional stencil consisting of a point and its four immediate neighbours on a rectangular grid 5059: 4912: 4452: 4041: 2278: 1492: 920: 764: 5580:— not-for-profit organisation that sets and maintains standards in computer-aided engineering analysis 5574:(MAthematics of Finite ELements and APplications) — international conference held at Brunel University 6795: 6743: 6614: 6347: 6324: 5894: 5802: 5701: 5603:— structural analysis method based on finite elements used to design reinforcement for concrete slabs 5146: 5140: 5072: 5053: 4838: 4771: 4470: 4464: 4333: 4257: 4246: 4131: 4121: 3937: 3823: 3754: 3410:— replaces constrained problems by unconstrained problems with a term added to the objective function 2685: 2664: 2434: 2382: 2295: 2281:— Cesàro means of partial sums of Fourier series converge uniformly for continuous periodic functions 2201: 2196: 2190:— continuous functions can be approximated uniformly by polynomials, or certain other function spaces 2181: 2127: 2068: 1770: 1640: 1620: 1613: 1543: 1487: 1401: 1290: 1276: 1091: 1024: 934: 848: 794: 782: 673: 551: 403: 338: 318: 264: 5210:— roughly, an ODE for which unstable methods need a very short step size, but stable methods do not 2838: 896:— example of a symmetric tridiagonal matrix with pairs of nearly, but not exactly, equal eigenvalues 6849: 6837: 6682: 6549: 6544: 6534: 6463: 6444: 6439: 6311: 6254: 6205: 6167: 6086: 5707: 5612: 5316: 5041: 4961: 4786:— adapting the subintervals in which the integration interval is divided depending on the integrand 4783: 4764: 4704: 4698: 4507: 4456: 4428: 4419: 4386: 4354: 4338: 4252: 4241: 4080: 3787: 3738: 3726: 3686: 3423: 3315: 2978: 2962: 2674: 2564: 2540: 2534: 2522: 2445: 2440: 2300: 2253: 2138: 2009: 1983: 1890: 1538: 1525: 1449: 1217: 995: 981: 960: 615: 485: 398: 348: 312: 306: 249: 129: 57: 43: 7049: 3617: 2853:— variation of simplex algorithm for problems with both "less than" and "greater than" constraints 1038:— variant which ensures that all entries remain integers if the initial matrix has integer entries 6990: 6985: 6626: 6589: 6578: 6528: 6492: 6486: 6361: 6280: 6233: 5626: 5322: 5065: 5047: 4811: 4629: 4402: 4230: 3988: 3642: 3399: 3363: 3069: 3032: 3017: 2916: 2813: 2743: 2546: 2080: 1931: 1835: 1497: 1114: 975: 952: 910: 843: 625: 600: 522: 511: 458: 428: 189: 33: 19: 6076:— artificial absorbing layer for wave equations, used to implement absorbing boundary conditions 5306:— stencil which only uses a few grid points, usually only the immediate and diagonal neighbours 4967: 4308:— find best approximation, constraint is that rank of some matrix is smaller than a given number 3393: 2622: 2616: 2592: 2516: 1873:
Methods for computing discrete convolutions with finite impulse response filters using the FFT:
1736:— can be thought of as a NURBS surface for which a row of control points is allowed to terminate 1681: 1162:— iterative procedure used to fit a generalized additive model, often equivalent to Gauss–Seidel 594: 589: 579: 541: 5384:— conservative scheme for hyperbolic system of conservation laws converges to the weak solution 7094: 7053: 7020: 7015: 6583: 6353: 6187: 6170:— subdivision into simplices, where vertices are not points but arbitrary sloped line segments 5889: 5704:— based on dividing the domain in many small domains; popular in computational fluid dynamics 5559: 5362: 5257: 5221: 5180: 5132:— divides interval in several subintervals and applies the shooting method on each subinterval 4673: 4328: 4311: 3783: 3488: 3267: 2945: 2880: 2827: 2787: 2759: 2610: 2334: 1989: 1856: 1690: 1520: 1512: 1426: 1385: 1318: 1312: 1302: 1273:— for finding solution with smallest 2-norm (for underdetermined systems) or smallest residual 1223: 1106: 1035: 899: 865: 838: 433: 142: 113: 49: 5698:— similar to the boundary element method, but the integral equation is evaluated analytically 5632: 5571: 5510:— a particular implementation of the finite element method, often used in structural analysis 3813: 2184:— function from given function space is determined uniquely by values on such a set of points 1261:
Underdetermined and overdetermined systems (systems that have no or more than one solution):
7045: 7010: 6539: 6335: 5964: 5859: 5765: 5684:(BEM) — based on transforming the PDE to an integral equation on the boundary of the domain 5617: 5577: 5500: 5081:— a method for the solution of Hamilton's equations that preserves the symplectic structure 4900: 4667: 4661: 4484: 4408: 4391: 4277: 4200: 4194: 4061: 3303: 3288: 2994: 2863: 2497: 2388: 2002: 1901: 1895: 1764: 1126: 1049: 1029: 1011: 946: 940: 893: 881: 860: 731: 464: 422: 259: 195: 119: 38: 6495:— uses a pre-computed table covering the probability distribution with rectangular segments 5710:— first-order conservative scheme for fluid flow, based on piecewise constant approximation 4140:— the maximum and maximizer are continuous as function of parameters, under some conditions 2287:— bounds distance between probability and Lebesgue measure in terms of Fourier coefficients 2238:— variant of Stone–Weierstrass theorem for polynomials if some coefficients have to be zero 2057:— the Nevanlinna–Pick interpolation has a solution if this matrix is positive semi-definite 6995: 6873: 6724: 6573: 6554: 6468: 6451: 6317: 6200: 6014:— preconditioner constructed with a structured mesh on a fictitious domain of simple shape 5675: 5662: 5450:— a finite element method in which the residual is orthogonal to the finite element space 5447: 5303: 5163: 5137:
Methods for solving differential-algebraic equations (DAEs), i.e., ODEs with constraints:
5124: 4894: 4635: 4137: 4092: 3849: 3476: 3297: 2940: 2772: 2767: 2348: 2340: 2217: 1936: 1507: 1416: 1409: 1343: 1297: 1264: 1253: 1229: 1120: 409: 343: 321:— contracting interval domains without removing any value consistent with the constraints 287: 6314:— diffusion introduced by the numerical method, above to that which is naturally present 4903:— either a second-order method with two stages, or a third-order method with three stages 4686: 3072:— extension of steepest descent for problems with a non-differentiable objective function 2832: 2363:— differential–algebraic equation whose solutions can approximate any continuous function 1663: 5476:— variant in which both the size and the order of the elements are automatically adapted 5101:— phenomenon that energy, which should be conserved, drifts away due to numerical errors 5035:— based on splitting ODE in a linear part, which is solved exactly, and a nonlinear part 2937:— set of integer vectors in a convex cone which generate all integer vectors in the cone 2256:— polynomials satisfying suitable 3-term recurrence relations are orthogonal polynomials 1898:— convolving any function with the Dirichlet kernel yields its trigonometric interpolant 7000: 6617:— produce multiple numerical predictions from slightly initial conditions or parameters 6521: 6417: 6274: 6211: 6114: 6017: 5731: 5513: 5207: 4489: 4434: 4414: 4007: 3828: 3413: 3196: 3057: 2792: 2778: 2528: 2366: 1861: 1658: 1626: 1279:— for finding the sparsest solution (i.e., the solution with as many zeros as possible) 1234: 1100: 890:— example of a matrix which is extremely ill-conditioned (and thus difficult to handle) 887: 853: 758: 417: 269: 168: 124: 52:— rate at which numerical solution of differential equation converges to exact solution 6147:— for any point, triangle containing it has nearest neighbour of the point as a vertex 5300:— the geometric arrangements of grid points affected by a basic step of the algorithm 5029:— combines the midpoint method with Richardson extrapolation to attain arbitrary order 4774:— variant of Gaussian quadrature which works well with singularities at the end points 3465:— uses "coarse" (ideal or low-fidelity) and "fine" (practical or high-fidelity) models 3429:
Reactive search optimization (RSO) — the algorithm adapts its parameters automatically
7073: 6980: 6920: 6830: 6820: 6192: 6102: 6090: 6026:— combines Neumann problem on one subdomain with Dirichlet problem on other subdomain 5848:(TLM) — based on analogy between electromagnetic field and mesh of transmission lines 5586:— technique based on finite elements for determining optimal composition of a mixture 5368: 4936: 4439: 4053: 3983: 3732: 3462: 3180: 3001: 2782: 2659: 2619:— fits a linear function times an exponential to last two iterates and their midpoint 2580: 2549:— a symmetric (but not necessarily positive definite) rank-one update of the Jacobian 2421: 2305: 2143: 2074: 1461: 1443: 1135: 828: 685: 517: 244: 5093:— variant of Euler method which is symplectic when applied to separable Hamiltonians 3639:— infinite number of variables and finite number of constraints, or other way around 3553:— initial state for certain optimal control problems with multiple optimal solutions 3514:(LQG) — system dynamics is a linear SDE with additive noise, objective is quadratic 2391:— about distance of points in a metric space from members of a sequence of subspaces 2110:— based on low-order polynomials of spatial coordinates; uses scattered observations 6181: 6096: 5931: 5725: 5713: 5535: 5098: 4921:— a fifth-order method with seven stages (FSAL) and an embedded fourth-order method 4864: 4494: 4344: 4172: 4013: 4001: 3432: 2850: 2841:— perturbed (hyper)cube; simplex method has exponential complexity on such a domain 1580: 1332: 1060: 923:— a distributed algorithm, especially suitable for processors laid out in a 2d grid 875: 719: 532: 6058:— variant of the problem which uses a discretization with fewer degrees of freedom 4909:— a third-order method with four stages (FSAL) and an embedded fourth-order method 4151:— approximating a given problem by an easier problem by relaxing some constraints 4044:— sufficient condition for strong duality to hold in a convex optimization problem 3332:(SQP) — replace problem by a quadratic programming problem, solve that, and repeat 3066:— use splitting of objective function in sum of possible non-differentiable pieces 2567:
method — truncated, matrix-free variant of BFGS method suitable for large problems
2531:— indicates which initial condition converges to which root under Newton iteration 2519:— based on linear approximation around the current iterate; quadratic convergence 2351:— application: replacing a function that is hard to evaluate by a simpler function 773:— iteration which converges quadratically to π, based on arithmetic–geometric mean 192:— discretizes a continuous equation by requiring it only to hold at certain points 6798:— used in numerical aeroacoustics to reduce sound sources to simple emitter types 5984:— abstract version of additive Schwarz without reference to geometric information 5734:— a solver for Riemann problems (a conservation law with piecewise constant data) 2337:— generalize Bernstein polynomials, SzĂĄsz–Mirakyan operators, and Lupas operators 284:— rounding a floating-point number by discarding all digits after a certain digit 116:
and global convergence — whether you need a good initial guess to get convergence
6975: 6175: 5973:— divides the domain in a few subdomains and solves the PDE on these subdomains 5333: 5213: 4817: 4023: 3746:— variant in which the algorithm parameters are adjusted during the computation. 3623: 3418: 3402:— derivative-free method, similar to Nelder–Mead but with guaranteed convergence 3278: 3272: 2096: 2054: 2035:(spherical linear interpolation) — interpolation between two points on a sphere 1749:— type of manifold parametrization used to smoothly join other surfaces together 1746: 833: 275: 225: 5292:— discrete analogue of the Poisson equation using the discrete Laplace operator 4032:— relates minimization problems with maximization problems of convex conjugates 3326:(SLP) — replace problem by a linear programming problem, solve that, and repeat 2561:— rank-two update of the Jacobian in which the matrix remains positive definite 712:— computes arithmetic–geometric mean; related methods compute special functions 597:— modification of the Horner scheme with more possibilities for parallelization 6868: 5919:— a method for solving elliptic PDEs by converting them to evolution equations 5910: 5015:— uses one method to approximate solution and another one to increase accuracy 4939:— algebraic formalism involving rooted trees for analysing Runge–Kutta methods 3550: 3120: 2738: 2613:— combines bisection method, secant method and inverse quadratic interpolation 2357:— field that studies connection between degree of approximation and smoothness 1708: 715: 709: 281: 5728:— limits spatial derivatives (fluxes) in order to avoid spurious oscillations 3426:— modification of search algorithms which builds up penalties during a search 2379:— condition guaranteeing that a measure is uniquely determined by its moments 7005: 6135:— triangulation such that no vertex is inside the circumcentre of a triangle 4325:— maximize the overall simulation efficiency for finding an optimal decision 3114: 3078:— generalization where objective function and constraint set can be biconvex 2991:— breaks up large QP problems into a series of smallest possible QP problems 2775:— contains all solutions that satisfy the constraints but may not be optimal 2071:— method for two-dimensional functions using Gaussians common in meteorology 315:— maps interval to subinterval which still contains the unknown exact answer 83:— similar to Aitken's delta-squared process, but applied to the partial sums 6338:— a functional-analytic reformulation of the PDE necessary for some methods 6283:— all vertices, line segments, triangles, tetrahedra, ..., making up a mesh 6123:— triangle mesh such that given set of point are all a vertex of a triangle 5609:— integrates finite elements into conventional NURBS-based CAD design tools 5087:— symplectic integrators derived using the underlying variational principle 5023:— a class of methods encapsulating linear multistep and Runge-Kutta methods 4958:— implicit methods of order 2 to 6; especially suitable for stiff equations 4933:— family of A-stable method with optimal order based on Gaussian quadrature 4341:— individuals make a series of two-period optimization decisions over time. 3765:— treats objective function as a random function and places a prior over it 3606:— class of pseudospectral method including Chebyshev, Legendre and knotting 3508:— system dynamics is a linear differential equation, objective is quadratic 3491:— equation for the "Lagrange multipliers" in Pontryagin's minimum principle 2244:— upper bound on L error of polynomial approximation in multiple dimensions 1648:— special case of cubic Hermite splines without self-intersections or cusps 1440:— computing the transpose of a matrix without using much additional storage 278:— extra precision introduced during a computation to reduce round-off error 6111:— subdivision of given region in triangles, or higher-dimensional analogue 6032:— domain decomposition methods that use Neumann problems on the subdomains 5928:— methods that respect in some sense the structure of the original problem 5886:— for vortex-dominated flows in fluid dynamics, similar to shock capturing 5796:(MFS) — represents solution as linear combination of fundamental solutions 5266:— table of coefficients of finite-difference approximations to derivatives 5253:— based on approximating differential operators with difference operators 4927:— a fifth-order method with six stages and an embedded fourth-order method 4915:— a fifth-order method with six stages and an embedded fourth-order method 2051:— interpolation by analytic functions in the unit disc subject to a bound 1587:
with unique polynomial interpolant and minimal growth of Lebesgue constant
1452:— methods that only access the matrix by evaluating matrix-vector products 978:— bidiagonal matrix of a certain form; generalizes the eigendecomposition 955:— rank-revealing QR factorization, can be used to compute rank of a matrix 6740:— computes averages of operators in many-body quantum mechanical problems 6597:— recursive filter suitable for problems with a large number of variables 5227: 1864:— the trigonometric constant coefficients that are multiplied by the data 1758: 1752: 1733: 1703: 1404:— analogue of Householder transformation for general inner product spaces 1340:— select a small submatrix which can be diagonalized exactly, and repeat 1226:(SIP — Strongly Implicit Procedure) — uses an incomplete LU decomposition 1052:— write a matrix as a product of an upper- and a lower-triangular matrix 728:— table of function values with unequal spacing to reduce round-off error 688:— shift-and-add algorithm using a table of logarithms and complex numbers 488:— the first algorithm which is faster than straightforward multiplication 7040:
Smith, N. J. J. (2008). "Worldly Vagueness and Semantic Indeterminacy".
6586:— improves sampling in physical systems with significant energy barriers 6277:— simply connected region between any three mutually tangent convex sets 6251:— improves Delauney triangularization by refining poor-quality triangles 5954:— for problems solution that can be related to an elastic grid behavior. 5748:— a method in which the elements can move freely relative to each other 2012:— constructed by recursively subdividing a piecewise linear interpolant 704:— modification of Stirling's approximation; easier to apply than Lanczos 670:
Elementary functions (exponential, logarithm, trigonometric functions):
6412:— sampling technique that uses Metropolis–Hastings to compute integrals 6225:— creates quality Delauney triangularization from piecewise linear data 6005: 5456:— a Galerkin method in which the approximate solution is not continuous 5437:— based on both the discretization of the solution and of its gradient 4233:— reconstruct a signal from knowledge that it is sparse or compressible 3582:— combines Ross–Fahroo pseudospectral method with differential flatness 2104:— constructs function on planar domain given its values on the boundary 1926: 160:
History of numerical solution of differential equations using computers
6184:— consists of congruent parallelograms, or higher-dimensional analogue 5678:— reduces the PDE to a large system of ordinary differential equations 5538:— particular grouping of finite elements, employed as a single element 5347:
Finite difference methods for hyperbolic PDEs like the wave equation:
4162:— ignoring the integrality constraints in a linear programming problem 2555:— update of the Jacobian in which the matrix remains positive definite 1773:— a unique, affine, symmetric map associated to a polynomial or spline 1434:— permutes rows/columns in sparse matrix to yield a narrow band matrix 6852:— used for simulating open quantum systems, operates on wave function 6038:— maps tangential electric field onto the equivalent electric current 5774:— based on minimization of weighted summation of the squared residual 5473: 4405:— solving dynamic programming problems by reasoning backwards in time 3799: 2888:— algorithm for specific LP problems (to find a weighted hitting set) 2437:— functions for which the interpolation problem has a unique solution 1853:— particular permutation of vectors with 2 entries used in many FFTs. 1798:— can be viewed as trigonometric interpolation at equidistant points 1366: 679: 548:
of D, and multiply that reciprocal by N to find the final quotient Q.
6858:(DDAM) — for evaluating effect of underwater explosions on equipment 6804:— uses Eulerian description for fluids and Lagrangian for structures 6489:— sample from a simpler distribution but reject some of the samples 6064:— uses the computed solution to refine the mesh only where necessary 4891:— one of the two main classes of methods for initial-value problems 4780:— based on expanding the integrand in terms of Chebyshev polynomials 4689:— sixth-order method, based on the values at five equidistant points 4676:— fourth-order method, based on (piecewise) quadratic approximation 4197:— the point minimizing the sum of distances to a given set of points 2525:— gives a region around solution such that Newton's method converges 2065:— the function being interpolated depends on more than one variable 929:— a randomized algorithm for checking the result of a multiplication 884:— symmetric positive definite with non-positive off-diagonal entries 779:— iteration which converges quartically to 1/π, and other algorithms 6070:— hierarchical method for evaluating particle-particle interactions 5526:— puts functions tailored to the problem in the approximation space 5224:— automatically changing the step size when that seems advantageous 5075:— a method that preserves some geometric structure of the equation 4860:— the numerical solution of ordinary differential equations (ODEs) 3240:— constraints include variational inequalities or complementarities 3218:(IRLS) — solves a weighted least-squares problem at every iteration 3142:— objective is ratio of nonlinear functions, constraints are linear 2267:— upper bound for best approximation by a trigonometric polynomial 1811:(FFT) — a fast method for computing the discrete Fourier transform 6483:— general and straightforward method but computationally expensive 5242:— the numerical solution of partial differential equations (PDEs) 5038:
Methods designed for the solution of ODEs from classical physics:
4751:— extension of Gaussian quadrature for integrals with weight exp(− 4737:— extension of Gaussian quadrature for integrals with weight (1 − 4727:— extension of Gaussian quadrature for integrals with weight exp(− 4203:— the centre of the smallest ball containing a given set of points 3547:— uses locally-quadratic models of the dynamics and cost functions 3254:— based on quadratic interpolation through the last three iterates 3224:— statistical techniques similar to principal components analysis 2220:— for constructing the best polynomial approximation in the L-norm 2032: 1044:— simplified form of Gaussian elimination for tridiagonal matrices 633: 6623:— for simulating the conformation and dynamics of polymer systems 6608:— to generate exit-points of Brownian motion from bounded domains 6344:— property of schemes that do not introduce spurious oscillations 5868:— considers solid particles as both numerical particles and fluid 5842:— semi-analytical Fourier-space method based on Floquet's theorem 5550:— discrete form of the exterior calculus of differential geometry 5200:— telescopic identity relating local and global truncation errors 4664:— first-order method, based on (piecewise) constant approximation 3614:— condition to make discretization and duality operations commute 3275:— the initial guess for a solution with which an algorithm starts 3136:— objective is ratio of linear functions, constraints are linear 1293:— a numerical algorithm for locating the eigenvalues of a matrix 1094:— procedure to turn an inaccurate solution in a more accurate one 998:— similarity transform bringing the matrix to a triangular matrix 718:(Fast E-function Evaluation) — fast summation of series like the 6883: 6518:— generates a random variable as a sum of other random variables 5999: 5993: 5719: 5544:
method — combination of finite elements with interval arithmetic
5216:— method is A-stable and stability function vanishes at infinity 4841:— approximates gradient of a function in an optimization problem 4670:— second-order method, based on (piecewise) linear approximation 4056:— for when objective function and constraints are differentiable 3559:— second-order condition for solution of optimal control problem 2077:— combination of linear interpolation and bilinear interpolation 1369:— Locally Optimal Block Preconditioned Conjugate Gradient Method 1063:— a special parallelized version of a LU decomposition algorithm 902:— square matrix whose successive powers approach the zero matrix 734:— algorithms that can compute individual digits of a real number 576:: for computing a number's multiplicative inverse (reciprocal). 469: 97:— book containing formulas and tables of many special functions 46:— the speed at which a convergent sequence approaches its limit 6296:— a consistent method is convergent if and only if it is stable 6236:— undirected graph formed by recursively subdividing a triangle 5990:(BDD) — preconditioner for symmetric positive definite matrices 5934:— models consisting of various submodels with different physics 3497:— minimum principle says that this function should be minimized 3090:— the most general optimization problem in the usual framework 2385:— condition that exponential sums are dense in weighted L space 5330:
Finite difference methods for heat equation and related PDEs:
5194:— local and global truncation errors, and their relationships 5172:— generalization of the family of Runge–Kutta methods for SDEs 5154:
Methods for solving stochastic differential equations (SDEs):
5121:
Methods for solving two-point boundary value problems (BVPs):
4467:— studies problems in which one problem is embedded in another 1832:— variant of Cooley–Tukey that uses a blend of radices 2 and 4 1014:— expressing a given matrix as a sum or difference of matrices 6406:— 1953 article proposing the Metropolis Monte Carlo algorithm 6208:— automatic procedure of generating meshes from 3D image data 5799:
Variants of MFS with source points on the physical boundary:
5768:— does not use a mesh, but uses a particle view of the field 5635:— functional space used in formulating the weakened weak form 4952:— the other main class of methods for initial-value problems 4713:— extension of Gaussian quadrature for integrals with weight 4181:— computational complexity of getting an approximate solution 3600:— generalization of pseudospectral methods in optimal control 3060:— row-action method for strictly convex optimization problems 2729:— algorithm for finding maxima or minima of a given function 2261:
Approximation by Fourier series / trigonometric polynomials:
2232:— generalization of Stone–Weierstrass theorem for polynomials 1208:— similar to CG but only assumed that the matrix is symmetric 992:— sum of commuting nilpotent matrix and diagonalizable matrix 963:— unitary matrix times positive-semidefinite Hermitian matrix 175:
International Workshops on Lattice QCD and Numerical Analysis
60:— methods to accelerate the speed of convergence of a series 5556:— solution of eigenvalue problems to find natural vibrations 4124:— method for solving (mixed) linear complementarity problems 3663:— finite number of variables, infinite number of constraints 3530:— matrix equation occurring in many optimal control problems 3117:— similar to polynomials, but exponents need not be integers 2170:— minimizes the maximum error over an interval (the L-norm) 1464:— construct a function going through some given data points 1375:— stability of eigenvalues under perturbations of the matrix 1032:— matrix in which all entries below a nonzero entry are zero 816:— study of numerical algorithms for linear algebra problems 5967:— uses a hierarchy of nested meshes to speed up the methods 4069:(KKT) — sufficient conditions for a solution to be optimal 2710:— tracking a root as one parameter in the equation changes 2250:— polynomials orthogonal with respect to a discrete measure 2226:— bound on maximum of derivative of polynomial in unit disk 1006:— unitary matrix times diagonal matrix times unitary matrix 791:— can be used to compute individual hexadecimal digits of π 749:— first algorithm that can compute π to arbitrary precision 89:— for accelerating the convergence of an alternating series 6044:— early and basic method on subdomains that do not overlap 5940:— for simulating elastic structures immersed within fluids 5740:— finite volume methods can be conservative, bounded, etc. 5629:— form of a PDE that is weaker than the standard weak form 5272:— finite-difference approximation of the Laplace operator 4873:— implicit methods need to solve an equation at every step 4314:— optimization of the parameters in an optimization method 3991:— convexity for functions defined on a Riemannian manifold 2607:— similar to Muller's method, but interpolates the inverse 2204:— basis of polynomials useful for approximating a function 1533:— for evaluating the interpolant; based on the Newton form 1148:(SOR) — a technique to accelerate the Gauss–Seidel method 767:— more complicated infinite product which converges faster 6746:— for multi-extremal optimization and importance sampling 6690:— uses a Green function to solve the Schrödinger equation 6404:
Equation of State Calculations by Fast Computing Machines
6265:— for finding triangle in a mesh containing a given point 5948:— extension of symplectic integrators, which are for ODEs 5760:— combination of cellular automata with discrete elements 5464:— a finite element method based on variational principles 4100:— study of problems with constraints of the form ⟨ 3345: 2595:— based on quadratic interpolation at last three iterates 514:— for computing quotient and/or remainder of two numbers 425:— error committed by doing only a finite numbers of steps 6117:— mesh in which all angles are less than or equal to 90° 4411:— choosing the optimal time to take a particular action 4038:— any function which relates to primal and dual problems 3735:— choose a point randomly in ball around current iterate 3300:— method that uses the gradient as the search direction 1220:— avoids inner products but needs bounds on the spectrum 972:— decomposition in terms of eigenvectors and eigenvalues 785:— fast algorithm that calculates a hypergeometric series 506:— asymptotically slightly faster than Schönhage–Strassen 6271:— dual representation of a mesh consisting of hexahedra 5532:— elements for describing functionally graded materials 5426:
Finite element methods, gradient discretisation methods
4620:{\displaystyle f(x,y)=(x^{2}+y-11)^{2}+(x+y^{2}-7)^{2}} 3485:— infinite-dimensional version of Lagrange multipliers 1802:
Relations between Fourier transforms and Fourier series
1446:— entry in a matrix on which the algorithm concentrates 1076:— for solving a system with a positive definite matrix 682:— shift-and-add algorithm using a table of arc tangents 6308:— all Fourier components of the error should be stable 5620:— finite-dimensional analogue of differential operator 5433:— based on a discretization of the space of solutions 5376:— first-order scheme for convection–diffusion problems 4707:— highest possible degree with given number of points 4510:— two-dimensional function with a banana-shaped valley 3520:— method for reducing dimension of LQG control problem 1321:— Arnoldi, specialized for positive-definite matrices 500:— based on Fourier transform, asymptotically very fast 5830:
Methods designed for problems from electromagnetics:
5276:
Eigenvalues and eigenvectors of the second derivative
4970: 4858:
Numerical methods for ordinary differential equations
4853:
Numerical methods for ordinary differential equations
4522: 4516:— two-dimensional with four local minima, defined by 4249:— an optimization technique for dispatching elevators 4214:— maximizing joint probability of Markov random field 3472:
Optimal control and infinite-dimensional optimization
3238:
Mathematical programming with equilibrium constraints
1921:— comparison of polynomial and rational interpolation 1552:— seventh-century formula for quadratic interpolation 1109:— for symmetric matrices, based on graph partitioning 6886:— direct inversion in (or of) the iterative subspace 6350:— linear monotone schemes can only be of first order 5235:
Numerical methods for partial differential equations
4701:— Richardson extrapolation applied to trapezium rule 4004:— dual solution gives a bound on the primal solution 3435:— majorize-minimization, a wide framework of methods 2589:— secant method with ideas from the bisection method 2583:— based on linear interpolation at last two iterates 2575:— uses divided differences instead of the derivative 2373:
points on a sphere that minimize some kind of energy
2176:— characterizes the best approximation in the L-norm 1242:— sparse approximation to the Cholesky factorization 1200:(BiCGSTAB) — variant of BiCG with better convergence 1186:— generalization for nonlinear optimization problems 1175:(CG) — assumes that the matrix is positive definite 6721:— entire sample is divided into equal-spin clusters 6639:— estimates the position and orientation of a robot 6257:— improves polynomial meshes by moving the vertices 6050:— early and basic method on subdomains that overlap 5336:(forward-time central-space) — first-order explicit 5278:— includes eigenvalues of discrete Laplace operator 5260:— the discrete analogue of a differential operator 4050:— concept of duality for integer linear programming 3536:— control that switches abruptly between two states 3372:— adapt coordinate directions to objective function 1123:— hybrid parallel solver for narrow-banded matrices 825:Types of matrices appearing in numerical analysis: 138:
Computational complexity of mathematical operations
5597:— for simulation of cracks and structural collapse 5284:— used for Laplace operator in multiple dimensions 5002: 4814:— uses a grid on a sphere with octahedral symmetry 4619: 4478:— finds a point in intersection of two convex sets 4175:— cost for increasing a variable by a small amount 3806:Simultaneous perturbation stochastic approximation 3655:— derivative with respect to changing in the shape 3205:— for constrained nonlinear least-squares problems 2820:) — objective function and constraints are linear 2762:— a constraint that involves exactly two variables 1761:— a monotone spline, defined in terms of M-splines 797:— faster version of Bailey–Borwein–Plouffe formula 412:— giving more significant figures than appropriate 6332:— the same, with resistivity instead of diffusion 5907:— for the solution of the Navier-Stokes equations 5754:— adds properties such as strain to each particle 5568:— simple test for the quality of a finite element 5143:— for solving Newton's equations with constraints 5106:Other methods for initial value problems (IVPs): 4632:— two-dimensional function with many local minima 4302:— find a point on a line by moving along the line 2395:Wirtinger's representation and projection theorem 1267:— find all solutions of an underdetermined system 461:— slightly worse than Kahan summation but cheaper 6936:Journal of Computational and Applied Mathematics 5419:— a finite-difference method for electrodynamics 4964:— fourth-order method for equations of the form 3831:— mimicks the improvisation process of musicians 3576:— uses Chebyshev polynomials (of the first kind) 2756:— studies optimization problems with constraints 1623:— the piecewise polynomials used as interpolants 165:Hundred-dollar, Hundred-digit Challenge problems 6817:(CMHD) — studies electrically conducting fluids 5854:— specifically designed for scattering problems 5444:— a physical approach to finite element methods 5062:— a two-step method extending the Verlet method 4808:(QSS) — based on the idea of state quantization 3626:— optimal control problem modelling advertising 3588:— uses collocation at the Legendre–Gauss points 3111:— problems involving signomials or posynomials 3020:— algorithm for solving basis pursuit denoising 1778:List of numerical computational geometry topics 1129:— eliminate even or odd rows or columns, repeat 755:— alternating series with very slow convergence 665:using details of the IEEE floating-point system 66:— most useful for linearly converging sequences 6952:Society for Industrial and Applied Mathematics 5183:— replaces the integral with a quadrature rule 4399:— continuous-time analogue of Bellman equation 3757:— deterministic variant of simulated annealing 3014:(BPDN) — regularized version of basis pursuit 3008:-norm of vector subject to linear constraints 2224:Bernstein's inequality (mathematical analysis) 1346:— the building block, almost a Givens rotation 1248:— sparse approximation to the LU factorization 1154:(SSOR) — variant of SOR for symmetric matrices 6394:— modification which allows larger step sizes 6214:— extracts a polygon mesh from a scalar field 5994:Balancing domain decomposition by constraints 5442:Finite element method in structural mechanics 5310:Higher-order compact finite difference scheme 5160:— generalization of the Euler method for SDEs 4026:— difference between primal and dual solution 3183:— the objective function is a sum of squares 2835:— rule to avoid cycling in the simplex method 2651:+ 1; generalizes Newton's and Halley's method 2471: 2113:Method based on polynomials are listed under 1791:— interpolation by trigonometric polynomials 203:— data structures for representing level sets 153:— combination of symbolic and numeric methods 8: 6727:— improvement of the Swendsen–Wang algorithm 6356:— benchmark problem for singularity problems 6153:— triangulation of minimum total edge length 5412:Finite difference methods for option pricing 4449:— there are multiple conflicting objectives 3682:Partially observable Markov decision process 3570:— based on Bellman's principle of optimality 1350:Jacobi method for complex Hermitian matrices 949:— orthogonal matrix times triangular matrix 494:— generalization of Karatsuba multiplication 103:— successor of book by Abramowitz and Stegun 5230:-- a parallel-in-time integration algorithm 3366:— move in one of the coordinate directions 3129:Quadratically constrained quadratic program 2083:— based on convolution with a sinc function 2044:Irrational base discrete weighted transform 1179:Derivation of the conjugate gradient method 761:— infinite product converging slowly to π/2 211:— methods based on the sinc function, sinc( 6643:Monte Carlo methods for electron transport 6567:Constructions of low-discrepancy sequences 5716:— second-order variant of Godunov's scheme 5044:— based on the extended mean-value theorem 4867:— the most basic method for solving an ODE 4761:— nested rule based on Gaussian quadrature 4657:— the numerical evaluation of an integral 4134:— used in the analysis of minimax problems 4010:— primal and dual solutions are equivalent 3228:Non-linear iterative partial least squares 2559:Broyden–Fletcher–Goldfarb–Shanno algorithm 2271:Bernstein's theorem (approximation theory) 1711:— multivariate generalization of B-splines 7050:10.1093/acprof:oso/9780199233007.003.0007 6500:For sampling from a normal distribution: 6302:— stability condition for hyperbolic PDEs 5374:Upwind differencing scheme for convection 4969: 4611: 4595: 4573: 4551: 4521: 3199:— variant of Gauss–Newton in econometrics 2543:— uses a rank-one update for the Jacobian 2537:— uses an approximation of the Jacobian: 1919:Polynomial and rational function modeling 1616:— interpolation by piecewise polynomials 1471:— takes the value of the nearest neighbor 943:— lower triangular times upper triangular 180:Timeline of numerical analysis after 1945 101:Digital Library of Mathematical Functions 6715:Methods for simulating the Ising model: 6428:Reversible-jump Markov chain Monte Carlo 5913:— for the solution of the Euler equation 5651:List of finite element software packages 5240:Numerical partial differential equations 5192:Truncation error (numerical integration) 5177:Methods for solving integral equations: 4792:— takes random samples of the integrand 4144:No free lunch in search and optimization 3123:— a signomial with positive coefficients 3094:Special cases of nonlinear programming: 2601:— higher-order variants of secant method 2500:— simple and robust; linear convergence 1767:— a spline fitted smoothly to noisy data 1327:— for when matrix is over a finite field 1214:(GMRES) — based on the Arnoldi iteration 7032: 6648:Monte Carlo method for photon transport 6000:Finite element tearing and interconnect 4897:— a second-order method with two stages 4834:Numerical smoothing and differentiation 4797: 3449:Ordered subset expectation maximization 2953:— list all vertices of the feasible set 2926:— solution at vertex of feasible region 1986:— a commonly used radial basis function 1357:Divide-and-conquer eigenvalue algorithm 676:— different methods for generating them 6907:For a large list of software, see the 6658:Monte Carlo methods for option pricing 6178:— consists of three-dimensional shapes 6159:— a triangulation that moves over time 5959:Techniques for improving these methods 5785:— represent continuum by a point cloud 5772:Discrete least squares meshless method 5690:— a version using interval arithmetics 5665:— based on the Fourier transformation 4879:— implicit variant of the Euler method 2482:— algorithms for solving the equation 2162:Least squares (function approximation) 1722:— generalizes De Casteljau's algorithm 1198:Biconjugate gradient stabilized method 907:Algorithms for matrix multiplication: 6802:Stochastic Eulerian Lagrangian method 6677:— incorporates Feynman path integrals 6400:— extension of Metropolis Monte Carlo 5988:Balancing domain decomposition method 5722:— advection upstream splitting method 5390:Alternating direction implicit method 5056:— another name for Verlet integration 4318:Multidisciplinary design optimization 4086:Lagrange multipliers on Banach spaces 3673:Approaches to deal with uncertainty: 3661:Generalized semi-infinite programming 3649:— optimization over a set of regions 3396:— based on conjugate gradient descent 1546:— especially useful for approximation 1517:Different forms for the interpolant: 878:— matrix composed of smaller matrices 7: 6962:SIAM Journal on Scientific Computing 6781:Numerical methods in fluid mechanics 6663:Quasi-Monte Carlo methods in finance 6368:Variants of the Monte Carlo method: 6105:— consists of triangles in 2D or 3D 5862:— used especially in fluid dynamics 5834:Finite-difference time-domain method 5789:Moving Particle Semi-implicit Method 5738:Properties of discretization schemes 5491:(CST) — also known as the T3 element 5417:Finite-difference time-domain method 5404:Nonstandard finite difference scheme 5282:Kronecker sum of discrete Laplacians 4117:Mixed linear complementarity problem 3348:Finding roots of nonlinear equations 3318:— mainly used for ill-posed problems 3216:Iteratively reweighted least squares 2464:Finding roots of nonlinear equations 2343:— approximation by sums of Gaussians 2273:— a converse to Jackson's inequality 2092:Nearest neighbor value interpolation 1678:Generalizations to more dimensions: 1152:Symmetric successive over-relaxation 1097:Direct methods for sparse matrices: 482:— general discussion, simple methods 293:Numeric precision in Microsoft Excel 6909:list of numerical-analysis software 6843:Numerical model of the Solar System 6516:Convolution random number generator 5996:(BDDC) — further development of BDD 5623:Combination with meshfree methods: 5470:— high-order finite element methods 5198:Lady Windermere's Fan (mathematics) 4323:Optimal computing budget allocation 4220:— used in the design of experiments 3356:Nonlinear conjugate gradient method 2924:Basic solution (linear programming) 2874:Mehrotra predictor–corrector method 2824:Algorithms for linear programming: 2330:SzĂĄsz–Mirakjan–Kantorovich operator 2164:— minimizes the error in the L-norm 2158:— measures smoothness of a function 1557:Extensions to multiple dimensions: 1550:Brahmagupta's interpolation formula 1265:Numerical computation of null space 1212:Generalized minimal residual method 1184:Nonlinear conjugate gradient method 1019:Solving systems of linear equations 984:— permutation of Jordan normal form 167:— list of ten problems proposed by 6957:SIAM Journal on Numerical Analysis 6815:Computational magnetohydrodynamics 6139:Constrained Delaunay triangulation 6099:— consists of polygons in 2D or 3D 5866:Multiphase particle-in-cell method 5396:-direction and then using flow in 5115:Partial element equivalent circuit 4650:Numerical quadrature (integration) 3444:Expectation–maximization algorithm 3252:Successive parabolic interpolation 2974:Linear least squares (mathematics) 2935:Hilbert basis (linear programming) 2847:— similar to the simplex algorithm 2637:''; achieves the cubic convergence 1992:— a specific polyharmonic spline: 1947:List of wavelet-related transforms 1943:List of functional analysis topics 371:— the relative difference between 14: 7090:Outlines of mathematics and logic 6300:Courant–Friedrichs–Lewy condition 6020:— meshes on subdomain do not mesh 5392:(ADI) — update using the flow in 5319:— any stencil that is not compact 5149:— for reducing the index of a DEA 4830:— for fractional-order integrals 4644:Mathematical Optimization Society 4638:— multimodal and multidimensional 3631:Infinite-dimensional optimization 3604:Ross–Fahroo pseudospectral method 3512:Linear-quadratic-Gaussian control 3148:Nonlinear complementarity problem 3052:Quadratic programming (see above) 2682:— fast, reliable, and widely used 2458:Interpolation (computer graphics) 2016:Catmull–Clark subdivision surface 1961:(RBF) — a function of the form ƒ( 1868:Cyclotomic fast Fourier transform 1240:Incomplete Cholesky factorization 648:Alpha max plus beta min algorithm 621:Methods of computing square roots 574:Multiplicative inverse Algorithms 156:Cultural and historical aspects: 6675:Path integral molecular dynamics 6129:— triangle mesh inside a polygon 5982:Abstract additive Schwarz method 5752:Extended discrete element method 5688:Interval boundary element method 5584:Multiphase topology optimisation 5489:Constant strain triangle element 5166:— a method with strong order one 4956:Backward differentiation formula 4759:Gauss–Kronrod quadrature formula 4397:Hamilton–Jacobi–Bellman equation 3545:Differential dynamic programming 3330:Sequential quadratic programming 2886:k-approximation of k-hitting set 2599:Sidi's generalized secant method 1103:— used in finite element methods 440:Elementary and special functions 326:Interval boundary element method 70:Minimum polynomial extrapolation 6808:Explicit algebraic stress model 6791:Smoothed-particle hydrodynamics 5846:Transmission-line matrix method 5794:Method of fundamental solutions 5495:Quadratic quadrilateral element 5130:Direct multiple shooting method 5050:— a popular second-order method 4695:— generalizes the above methods 4502:Test functions for optimization 3793:Genetic algorithms in economics 3574:Chebyshev pseudospectral method 3336:Newton's method in optimization 3203:Generalized Gauss–Newton method 2989:Sequential minimal optimization 2605:Inverse quadratic interpolation 2553:Davidon–Fletcher–Powell formula 2506:— variant for complex functions 2408:Journal of Approximation Theory 2361:Universal differential equation 2168:Minimax approximation algorithm 1483:— interpolation by polynomials 1457:Interpolation and approximation 1085:Symbolic Cholesky decomposition 7042:Vagueness and Degrees of Truth 6856:Dynamic design analysis method 6770:Computational electromagnetics 6670:Monte Carlo molecular modeling 6653:Monte Carlo methods in finance 6306:Von Neumann stability analysis 6163:Triangulated irregular network 5840:Rigorous coupled-wave analysis 5639:Smoothed finite element method 5524:Extended finite element method 5497:— also known as the Q8 element 5485:— also known as the Q4 element 5483:Bilinear quadrilateral element 5435:gradient discretisation method 4997: 4985: 4885:— second-order implicit method 4806:Quantized state systems method 4608: 4582: 4570: 4544: 4538: 4526: 4476:Dykstra's projection algorithm 3598:Pseudospectral knotting method 3592:Legendre pseudospectral method 3563:Pseudospectral optimal control 3483:Pontryagin's minimum principle 2894:Linear complementarity problem 2248:Discrete Chebyshev polynomials 2193:Approximation by polynomials: 2087:Natural neighbor interpolation 1646:Centripetal Catmull–Rom spline 1629:— polynomial spline of degree 1469:Nearest-neighbor interpolation 990:Jordan–Chevalley decomposition 966:Decompositions by similarity: 916:Coppersmith–Winograd algorithm 789:Bailey–Borwein–Plouffe formula 612:Square roots and other roots: 369:Relative change and difference 300:Arbitrary-precision arithmetic 87:Van Wijngaarden transformation 64:Aitken's delta-squared process 1: 6930:American Mathematical Society 6731:Metropolis–Hastings algorithm 6476:Pseudo-random number sampling 6387:Metropolis–Hastings algorithm 6372:Direct simulation Monte Carlo 6008:— further development of FETI 5917:Relaxation (iterative method) 5852:Uniform theory of diffraction 5646:Variational multiscale method 5479:Examples of finite elements: 5454:Discontinuous Galerkin method 5264:Finite difference coefficient 4871:Explicit and implicit methods 4160:Linear programming relaxation 4112:Mixed complementarity problem 4067:Karush–Kuhn–Tucker conditions 3568:Bellman pseudospectral method 3389:Pattern search (optimization) 3324:Successive linear programming 3211:Levenberg–Marquardt algorithm 3134:Linear-fractional programming 3043:Second-order cone programming 2714:Piecewise linear continuation 2647:derivatives to achieve order 2049:Nevanlinna–Pick interpolation 2021:Doo–Sabin subdivision surface 1914:Simple rational approximation 1728:Non-uniform rational B-spline 1438:In-place matrix transposition 1380:Other concepts and algorithms 1168:Modified Richardson iteration 567:Addition-chain exponentiation 362:Residual (numerical analysis) 6826:Numerical weather prediction 6775:Computational fluid dynamics 6694:Gaussian quantum Monte Carlo 6245:Improving an existing mesh: 6195:— isotropic grid on a sphere 6151:Minimum-weight triangulation 5971:Domain decomposition methods 5836:— a finite-difference method 5566:Patch test (finite elements) 5530:Functionally graded elements 5298:Stencil (numerical analysis) 4447:Multi-objective optimization 4218:Response surface methodology 3744:Adaptive simulated annealing 3518:Optimal projection equations 3495:Hamiltonian (control theory) 2912:Theory of two-level planning 2355:Constructive function theory 2308:— table of PadĂ© approximants 2210:— error when approximating | 1870:— for FFT over finite fields 1654:Monotone cubic interpolation 1603:Abel–Goncharov interpolation 1042:Tridiagonal matrix algorithm 1004:Singular value decomposition 801:List of formulae involving π 498:Schönhage–Strassen algorithm 239:Error analysis (mathematics) 186:General classes of methods: 151:Symbolic-numeric computation 6738:Auxiliary field Monte Carlo 6342:Total variation diminishing 5815:Regularized meshless method 4943:List of Runge–Kutta methods 4925:Runge–Kutta–Fehlberg method 4295:Linear programming decoding 4268:Hyperparameter optimization 4075:— variant of KKT conditions 3819:Particle swarm optimization 3720:Stochastic gradient descent 3701:— constraints are uncertain 3594:— uses Legendre polynomials 3586:Gauss pseudospectral method 3408:Augmented Lagrangian method 3370:Adaptive coordinate descent 3309:Stochastic gradient descent 3048:Sum-of-squares optimization 2930:Fourier–Motzkin elimination 2907:Dantzig–Wolfe decomposition 2326:on a semi-infinite interval 2149:Vector field reconstruction 1789:Trigonometric interpolation 1784:Trigonometric interpolation 1338:Jacobi eigenvalue algorithm 1315:— based on Krylov subspaces 1308:Rayleigh quotient iteration 1271:Moore–Penrose pseudoinverse 1246:Incomplete LU factorization 1192:Biconjugate gradient method 201:Level set (data structures) 7116: 6926:Mathematics of Computation 6632:Metropolis light transport 6481:Inverse transform sampling 6435:Dynamic Monte Carlo method 6048:Schwarz alternating method 5946:Multisymplectic integrator 5922:Broad classes of methods: 5758:Movable cellular automaton 5548:Discrete exterior calculus 5091:Semi-implicit Euler method 5013:Predictor–corrector method 5003:{\displaystyle y''=f(t,y)} 4778:Clenshaw–Curtis quadrature 4711:Chebyshev–Gauss quadrature 4382:Combinatorial optimization 4263:Highly optimized tolerance 4212:Iterated conditional modes 4149:Relaxation (approximation) 3668:Uncertainty and randomness 3580:Flat pseudospectral method 3557:Legendre–Clebsch condition 3540:Covector mapping principle 3528:Algebraic Riccati equation 3506:Linear-quadratic regulator 2951:Vertex enumeration problem 2427:Linear predictive analysis 2403:Constructive Approximation 2292:Different approximations: 2063:Multivariate interpolation 1954:Inverse distance weighting 1841:Prime-factor FFT algorithm 1825:Cooley–Tukey FFT algorithm 1796:Discrete Fourier transform 1422:Block matrix pseudoinverse 1397:Householder transformation 1256:— for saddle node problems 1146:Successive over-relaxation 1056:Crout matrix decomposition 871:Diagonally dominant matrix 562:Exponentiation by squaring 357:Propagation of uncertainty 7085:Mathematics-related lists 6941:BIT Numerical Mathematics 6879:Density functional theory 6753:list of statistics topics 6699:Path integral Monte Carlo 6457:Auxiliary particle filter 6398:Wang and Landau algorithm 6036:Poincaré–Steklov operator 5905:Lattice Boltzmann methods 5290:Discrete Poisson equation 5270:Discrete Laplace operator 5246:Finite difference methods 5110:Bi-directional delay line 4828:Numerical differentiation 4749:Gauss–Laguerre quadrature 4680:Adaptive Simpson's method 4283:Extended newsvendor model 4273:Inventory control problem 4226:Automatic label placement 4179:Hardness of approximation 4030:Fenchel's duality theorem 3637:Semi-infinite programming 3439:Least absolute deviations 3376:Random coordinate descent 3243:Univariate optimization: 2727:Mathematical optimization 2656:Methods for polynomials: 2472:#Numerical linear algebra 2314:Hartogs–Rosenthal theorem 2188:Stone–Weierstrass theorem 2102:Transfinite interpolation 1830:Split-radix FFT algorithm 1815:Bluestein's FFT algorithm 1206:Conjugate residual method 1173:Conjugate gradient method 650:— approximates hypot(x,y) 454:Kahan summation algorithm 255:Catastrophic cancellation 6897:Computational statistics 6637:Monte Carlo localization 6601:Transition path sampling 6562:Low-discrepancy sequence 6382:Markov chain Monte Carlo 6377:Quasi-Monte Carlo method 6218:Parallel mesh generation 6109:Triangulation (geometry) 6062:Adaptive mesh refinement 6024:Neumann–Dirichlet method 6012:Fictitious domain method 5938:Immersed boundary method 5821:Singular boundary method 5809:Boundary particle method 5554:Modal analysis using FEM 5251:Finite difference method 5170:Runge–Kutta method (SDE) 5027:Bulirsch–Stoer algorithm 4725:Gauss–Hermite quadrature 4350:Space allocation problem 4288:Assemble-to-order system 4168:Self-concordant function 4019:Dual cone and polar cone 3779:Evolutionary programming 3705:Stochastic approximation 3360:Derivative-free methods 3284:Backtracking line search 3187:Non-linear least squares 3064:Proximal gradient method 3038:Semidefinite programming 3028:Linear matrix inequality 2754:Constrained optimization 2749:Constraint (mathematics) 2453:Curve-fitting compaction 2115:Polynomial interpolation 2026:Loop subdivision surface 1851:Bit-reversal permutation 1715:Truncated power function 1669:De Casteljau's algorithm 1481:Polynomial interpolation 1476:Polynomial interpolation 1080:Minimum degree algorithm 814:Numerical linear algebra 809:Numerical linear algebra 771:Gauss–Legendre algorithm 654:Fast inverse square root 606:De Casteljau's algorithm 492:Toom–Cook multiplication 480:Multiplication algorithm 76:Richardson extrapolation 6892:Computational sociology 6864:Computational chemistry 6719:Swendsen–Wang algorithm 6709:Variational Monte Carlo 6410:Multicanonical ensemble 6392:Multiple-try Metropolis 6294:Lax equivalence theorem 6269:Spatial twist continuum 6263:Jump-and-Walk algorithm 6249:Chew's second algorithm 6240:Barycentric subdivision 6121:Point-set triangulation 6074:Perfectly matched layer 6042:Schur complement method 6030:Neumann–Neumann methods 5977:Additive Schwarz method 5746:Discrete element method 5696:Analytic element method 5682:Boundary element method 5590:Interval finite element 5542:Interval finite element 5519:Finite element updating 5508:Direct stiffness method 5468:Spectral element method 5408:Specific applications: 5365:— second-order explicit 5359:— second-order explicit 5342:— second-order implicit 4950:Linear multistep method 4907:Bogacki–Shampine method 4847:Euler–Maclaurin formula 4790:Monte Carlo integration 4735:Gauss–Jacobi quadrature 4370:Wing-shape optimization 4360:Trajectory optimization 3710:Stochastic optimization 3677:Markov decision process 3458:Nearest neighbor search 3012:Basis pursuit denoising 2798:Continuous optimization 2691:Splitting circle method 2680:Jenkins–Traub algorithm 2320:SzĂĄsz–Mirakyan operator 2174:Equioscillation theorem 2134:Orders of approximation 1755:— a non-negative spline 1742:Kochanek–Bartels spline 1566:Trilinear interpolation 1432:Cuthill–McKee algorithm 1373:Eigenvalue perturbation 1325:Block Lanczos algorithm 1117:— for Toeplitz matrices 538:Newton–Raphson division 330:Interval finite element 109:Curse of dimensionality 6621:Bond fluctuation model 6606:Walk-on-spheres method 6595:Ensemble Kalman filter 6509:Marsaglia polar method 6423:Coupling from the past 6145:Pitteway triangulation 6133:Delaunay triangulation 5900:Orthogonal collocation 5879:Shock capturing method 5874:High-resolution scheme 5783:Finite pointset method 5778:Diffuse element method 5669:Pseudo-spectral method 5595:Applied element method 5353:— first-order explicit 5085:Variational integrator 5033:Exponential integrator 5021:General linear methods 5004: 4823:Coopmans approximation 4621: 4481:Algorithmic concepts: 4306:Low-rank approximation 4098:Complementarity theory 4048:Total dual integrality 3997:Duality (optimization) 3774:Differential evolution 3769:Evolutionary algorithm 3750:Great Deluge algorithm 3715:Stochastic programming 3653:Topological derivative 3192:Gauss–Newton algorithm 3140:Fractional programming 2902:Benders' decomposition 2708:Numerical continuation 2701:Wilkinson's polynomial 2504:Lehmer–Schur algorithm 2480:Root-finding algorithm 2429:— linear extrapolation 2285:ErdƑs–TurĂĄn inequality 2108:Trend surface analysis 1809:Fast Fourier transform 1674:composite BĂ©zier curve 1598:Birkhoff interpolation 1576:Tricubic interpolation 1561:Bilinear interpolation 1362:Folded spectrum method 1074:Cholesky decomposition 1069:Block LU decomposition 702:Spouge's approximation 528:Non-restoring division 446:Unrestricted algorithm 209:Sinc numerical methods 72:— for vector sequences 6946:Numerische Mathematik 6786:Large eddy simulation 6765:Computational physics 6704:Reptation Monte Carlo 6688:Diffusion Monte Carlo 6330:Numerical resistivity 6157:Kinetic triangulation 6127:Polygon triangulation 6068:Fast multipole method 5952:Stretched grid method 5884:Vorticity confinement 5607:Isogeometric analysis 5431:Finite element method 5351:Lax–Friedrichs method 5340:Crank–Nicolson method 5158:Euler–Maruyama method 5079:Symplectic integrator 5005: 4931:Gauss–Legendre method 4919:Dormand–Prince method 4877:Backward Euler method 4693:Newton–Cotes formulas 4655:Numerical integration 4622: 4514:Himmelblau's function 4365:Transportation theory 4300:Linear search problem 4237:Cutting stock problem 4155:Lagrangian relaxation 4073:Fritz John conditions 4036:Perturbation function 3900:Pseudoconvex function 3834:see also the section 3763:Bayesian optimization 3699:Scenario optimization 3647:Topology optimization 3247:Golden section search 3222:Partial least squares 3109:Geometric programming 3088:Nonlinear programming 3083:Nonlinear programming 3076:Biconvex optimization 2984:Frank–Wolfe algorithm 2969:Quadratic programming 2869:Karmarkar's algorithm 2859:Interior point method 2845:Criss-cross algorithm 2803:Discrete optimization 2587:False position method 2512:Fixed-point iteration 2322:— approximation by e 2242:Bramble–Hilbert lemma 2156:Modulus of continuity 1959:Radial basis function 1846:Rader's FFT algorithm 1820:Bruun's FFT algorithm 1684:— maps a triangle to 1593:Hermite interpolation 1571:Bicubic interpolation 1503:Chebyshev polynomials 1286:Eigenvalue algorithms 1160:Backfitting algorithm 935:Matrix decompositions 753:Leibniz formula for π 747:Liu Hui's π algorithm 726:Gal's accurate tables 697:Lanczos approximation 95:Abramowitz and Stegun 81:Shanks transformation 7044:. pp. 277–316. 6796:Aeroacoustic analogy 6744:Cross-entropy method 6615:Ensemble forecasting 6504:Box–Muller transform 6325:Numerical dispersion 5895:Fast marching method 5803:Boundary knot method 5702:Finite volume method 5462:Rayleigh–Ritz method 5382:Lax–Wendroff theorem 5147:Pantelides algorithm 5141:Constraint algorithm 5073:Geometric integrator 5054:Leapfrog integration 4968: 4839:Adjoint state method 4772:Tanh-sinh quadrature 4520: 4471:Optimal substructure 4465:Bilevel optimization 4334:Process optimization 4258:Entropy maximization 4247:Destination dispatch 3938:Quasiconvex function 3824:Stochastic tunneling 3755:Mean field annealing 3692:Wald's maximin model 3378:— randomized version 3261:General algorithms: 2670:Durand–Kerner method 2641:Householder's method 2474:for linear equations 2435:Unisolvent functions 2377:Carleman's condition 2296:Moving least squares 2265:Jackson's inequality 2208:Bernstein's constant 2202:Bernstein polynomial 2197:Linear approximation 2182:Unisolvent point set 2128:Approximation theory 2123:Approximation theory 2069:Barnes interpolation 1771:Blossom (functional) 1641:Cubic Hermite spline 1621:Spline (mathematics) 1614:Spline interpolation 1609:Spline interpolation 1544:Bernstein polynomial 1488:Linear interpolation 1402:Householder operator 1392:Gram–Schmidt process 1291:Eigenvalue algorithm 1277:Sparse approximation 1092:Iterative refinement 1025:Gaussian elimination 927:Freivalds' algorithm 849:Pentadiagonal matrix 783:Chudnovsky algorithm 674:Trigonometric tables 552:Goldschmidt division 404:Artificial precision 339:Loss of significance 319:Interval propagation 265:Discretization error 6850:Quantum jump method 6838:Celestial mechanics 6683:Quantum Monte Carlo 6550:Stratified sampling 6545:Importance sampling 6535:Antithetic variates 6464:Reverse Monte Carlo 6445:Gillespie algorithm 6440:Kinetic Monte Carlo 6312:Numerical diffusion 6255:Laplacian smoothing 6223:Ruppert's algorithm 6206:Image-based meshing 6168:Quasi-triangulation 6087:Grid classification 5613:Loubignac iteration 5357:Lax–Wendroff method 5317:Non-compact stencil 5042:Newmark-beta method 4889:Runge–Kutta methods 4798:#Monte Carlo method 4784:Adaptive quadrature 4765:Gauss–Kronrod rules 4705:Gaussian quadrature 4508:Rosenbrock function 4457:vector optimization 4429:Global optimization 4387:Dynamic programming 4355:Stress majorization 4339:Recursive economics 4253:Energy minimization 4242:Demand optimization 4081:Lagrange multiplier 3844:Theoretical aspects 3788:Genetic programming 3739:Simulated annealing 3727:Random optimization 3687:Robust optimization 3502:Types of problems: 3424:Guided Local Search 3316:Landweber iteration 3103:Convex optimization 2979:Total least squares 2963:Convex optimization 2958:Convex optimization 2818:integer programming 2573:Steffensen's method 2565:Limited-memory BFGS 2535:Quasi-Newton method 2523:Kantorovich theorem 2446:Isotonic regression 2441:Regression analysis 2236:MĂŒntz–SzĂĄsz theorem 2230:Mergelyan's theorem 2010:Subdivision surface 1984:Polyharmonic spline 1891:Sigma approximation 1882:Overlap–save method 1720:De Boor's algorithm 1693:— maps a square to 1583:— set of points in 1539:Lagrange polynomial 1531:Neville's algorithm 1526:Divided differences 1450:Matrix-free methods 1218:Chebyshev iteration 1141:Gauss–Seidel method 1132:Iterative methods: 996:Schur decomposition 982:Weyr canonical form 961:Polar decomposition 777:Borwein's algorithm 616:Integer square root 486:Karatsuba algorithm 399:Significant figures 353:Error propagation: 349:Numerical stability 313:Interval contractor 307:Interval arithmetic 250:Approximation error 130:Difference quotient 58:Series acceleration 44:Rate of convergence 7080:Numerical analysis 6996:Nicholas J. Higham 6991:Margaret H. Wright 6986:James H. Wilkinson 6950:Journals from the 6928:(published by the 6627:Iterated filtering 6590:Hybrid Monte Carlo 6579:Parallel tempering 6529:Variance reduction 6493:Ziggurat algorithm 6487:Rejection sampling 6362:Monte Carlo method 6281:Simplicial complex 6234:Apollonian network 5627:Weakened weak form 5323:Five-point stencil 5066:Dynamic relaxation 5060:Beeman's algorithm 5048:Verlet integration 5000: 4812:Lebedev quadrature 4630:Rastrigin function 4617: 4453:Benson's algorithm 4403:Backward induction 4231:Compressed sensing 4042:Slater's condition 3989:Geodesic convexity 3836:Monte Carlo method 3643:Shape optimization 3400:Rosenbrock methods 3384:Nelder–Mead method 3364:Coordinate descent 3099:Linear programming 3070:Subgradient method 3033:Conic optimization 3018:In-crowd algorithm 2917:Variable splitting 2814:Linear programming 2809:Linear programming 2744:Candidate solution 2547:Symmetric rank-one 2081:Lanczos resampling 1932:Continuous wavelet 1908:Other interpolants 1877:Overlap–add method 1836:Goertzel algorithm 1513:Lebesgue constants 1498:Vandermonde matrix 1493:Runge's phenomenon 1115:Levinson recursion 976:Jordan normal form 970:Eigendecomposition 953:RRQR factorization 921:Cannon's algorithm 911:Strassen algorithm 844:Tridiagonal matrix 738:Approximations of 601:Clenshaw algorithm 523:Restoring division 512:Division algorithm 459:Pairwise summation 429:Well-posed problem 190:Collocation method 34:Validated numerics 20:numerical analysis 7021:Vladik Kreinovich 7016:Ulrich W. Kulisch 6584:Umbrella sampling 6348:Godunov's theorem 6188:Unstructured grid 5890:Split-step method 5601:Wood–Armer method 5363:MacCormack method 5258:Finite difference 5222:Adaptive stepsize 4329:Paper bag problem 4312:Meta-optimization 4132:Danskin's theorem 4122:Lemke's algorithm 3784:Genetic algorithm 3612:Ross–Fahroo lemma 3534:Bang–bang control 3489:Costate equations 3268:Descent direction 2946:Linear inequality 2881:Column generation 2828:Simplex algorithm 2788:Maxima and minima 2760:Binary constraint 2686:Laguerre's method 2665:Bairstow's method 2494:General methods: 2383:Krein's condition 2335:Baskakov operator 2214:| by a polynomial 1990:Thin plate spline 1857:Butterfly diagram 1637:th derivate is ±1 1521:Newton polynomial 1427:Bidiagonalization 1386:Orthogonalization 1319:Lanczos algorithm 1313:Arnoldi iteration 1303:Inverse iteration 1107:Nested dissection 1036:Bareiss algorithm 900:Convergent matrix 866:Triangular matrix 839:Bidiagonal matrix 795:Bellard's formula 656:— calculates 1 / 629:th root algorithm 504:FĂŒrer's algorithm 434:Affine arithmetic 143:Smoothed analysis 114:Local convergence 50:Order of accuracy 7107: 7064: 7063: 7037: 7011:Richard S. Varga 6540:Control variates 6336:Weak formulation 6081:Grids and meshes 5965:Multigrid method 5860:Particle-in-cell 5766:Meshfree methods 5708:Godunov's scheme 5618:Stiffness matrix 5501:Barsoum elements 5009: 5007: 5006: 5001: 4978: 4962:Numerov's method 4913:Cash–Karp method 4883:Trapezoidal rule 4720: 4699:Romberg's method 4668:Trapezoidal rule 4662:Rectangle method 4626: 4624: 4623: 4618: 4616: 4615: 4600: 4599: 4578: 4577: 4556: 4555: 4485:Barrier function 4420:Robbins' problem 4409:Optimal stopping 4392:Bellman equation 4278:Newsvendor model 4201:Chebyshev center 4195:Geometric median 3342:Newton algorithm 3304:Gradient descent 3289:Wolfe conditions 2995:Bilinear program 2898:Decompositions: 2864:Ellipsoid method 2675:Graeffe's method 2541:Broyden's method 2498:Bisection method 2389:Lethargy theorem 2301:PadĂ© approximant 2254:Favard's theorem 2139:Lebesgue's lemma 2003:Hierarchical RBF 1902:Gibbs phenomenon 1896:Dirichlet kernel 1765:Smoothing spline 1127:Cyclic reduction 1050:LU decomposition 1030:Row echelon form 1012:Matrix splitting 947:QR decomposition 941:LU decomposition 894:Wilkinson matrix 882:Stieltjes matrix 861:Circulant matrix 741: 732:Spigot algorithm 693:Gamma function: 664: 663: 636:— the function ( 558:Exponentiation: 476:Multiplication: 465:Binary splitting 423:Truncation error 260:Condition number 196:Level-set method 120:Superconvergence 39:Iterative method 7115: 7114: 7110: 7109: 7108: 7106: 7105: 7104: 7100:Lists of topics 7070: 7069: 7068: 7067: 7060: 7039: 7038: 7034: 7029: 6972: 6917: 6905: 6874:Coupled cluster 6761: 6725:Wolff algorithm 6574:Event generator 6555:VEGAS algorithm 6469:Demon algorithm 6452:Particle filter 6365: 6318:False diffusion 6290: 6201:Mesh generation 6083: 5961: 5926:Mimetic methods 5676:Method of lines 5663:Spectral method 5659: 5448:Galerkin method 5428: 5304:Compact stencil 5248: 5237: 5164:Milstein method 5125:Shooting method 4971: 4966: 4965: 4895:Midpoint method 4855: 4714: 4652: 4636:Shekel function 4607: 4591: 4569: 4547: 4518: 4517: 4378: 4208:In statistics: 4188: 4138:Maximum theorem 4093:Semi-continuity 3850:Convex analysis 3846: 3670: 3477:Optimal control 3474: 3394:Powell's method 3340:See also under 3298:Gradient method 3085: 3007: 2960: 2941:LP-type problem 2839:Klee–Minty cube 2811: 2773:Feasible region 2768:Corner solution 2735: 2724: 2623:Halley's method 2617:Ridders' method 2593:Muller's method 2517:Newton's method 2466: 2418: 2349:Surrogate model 2341:Favard operator 2279:FejĂ©r's theorem 2218:Remez algorithm 2125: 1979: 1937:Transfer matrix 1910: 1786: 1682:BĂ©zier triangle 1611: 1508:Chebyshev nodes 1478: 1459: 1417:Krylov subspace 1410:Givens rotation 1382: 1344:Jacobi rotation 1298:Power iteration 1288: 1254:Uzawa iteration 1230:Kaczmarz method 1121:SPIKE algorithm 1021: 822: 811: 765:ViĂšte's formula 739: 659: 657: 595:Estrin's scheme 590:Horner's method 580:Newton's method 542:Newton's method 442: 410:False precision 344:Numerical error 288:Round-off error 236: 30: 12: 11: 5: 7113: 7111: 7103: 7102: 7097: 7092: 7087: 7082: 7072: 7071: 7066: 7065: 7058: 7031: 7030: 7028: 7025: 7024: 7023: 7018: 7013: 7008: 7003: 7001:Nick Trefethen 6998: 6993: 6988: 6983: 6978: 6971: 6968: 6967: 6966: 6965: 6964: 6959: 6948: 6943: 6938: 6933: 6923: 6916: 6913: 6904: 6901: 6900: 6899: 6894: 6889: 6888: 6887: 6881: 6876: 6871: 6861: 6860: 6859: 6853: 6847: 6846: 6845: 6835: 6834: 6833: 6823: 6818: 6812: 6811: 6810: 6805: 6799: 6793: 6788: 6783: 6772: 6760: 6757: 6756: 6755: 6749: 6748: 6747: 6741: 6735: 6734: 6733: 6728: 6722: 6713: 6712: 6711: 6706: 6701: 6696: 6691: 6680: 6679: 6678: 6667: 6666: 6665: 6660: 6650: 6645: 6640: 6634: 6629: 6624: 6618: 6611:Applications: 6609: 6603: 6598: 6592: 6587: 6581: 6576: 6571: 6570: 6569: 6559: 6558: 6557: 6552: 6547: 6542: 6537: 6526: 6525: 6524: 6522:Indexed search 6519: 6513: 6512: 6511: 6506: 6498: 6497: 6496: 6484: 6473: 6472: 6471: 6466: 6461: 6460: 6459: 6449: 6448: 6447: 6442: 6432: 6431: 6430: 6425: 6420: 6418:Gibbs sampling 6415: 6414: 6413: 6407: 6401: 6395: 6379: 6374: 6364: 6359: 6358: 6357: 6354:Motz's problem 6351: 6345: 6339: 6333: 6327: 6322: 6321: 6320: 6309: 6303: 6297: 6289: 6286: 6285: 6284: 6278: 6275:Pseudotriangle 6272: 6266: 6260: 6259: 6258: 6252: 6243: 6237: 6231: 6228: 6227: 6226: 6220: 6215: 6212:Marching cubes 6209: 6198: 6197: 6196: 6190: 6185: 6179: 6173: 6172: 6171: 6165: 6160: 6154: 6148: 6142: 6136: 6130: 6124: 6118: 6115:Nonobtuse mesh 6112: 6100: 6082: 6079: 6078: 6077: 6071: 6065: 6059: 6053: 6052: 6051: 6045: 6039: 6033: 6027: 6021: 6018:Mortar methods 6015: 6009: 6003: 5997: 5991: 5985: 5979: 5968: 5960: 5957: 5956: 5955: 5949: 5943: 5942: 5941: 5935: 5929: 5920: 5914: 5908: 5902: 5897: 5892: 5887: 5881: 5876: 5871: 5870: 5869: 5857: 5856: 5855: 5849: 5843: 5837: 5828: 5827: 5826: 5825: 5824: 5818: 5812: 5806: 5797: 5791: 5786: 5780: 5775: 5763: 5762: 5761: 5755: 5743: 5742: 5741: 5735: 5732:Riemann solver 5729: 5723: 5717: 5711: 5699: 5693: 5692: 5691: 5679: 5673: 5672: 5671: 5658: 5655: 5654: 5653: 5648: 5643: 5642: 5641: 5636: 5630: 5621: 5615: 5610: 5604: 5598: 5592: 5587: 5581: 5575: 5569: 5563: 5557: 5551: 5545: 5539: 5533: 5527: 5521: 5516: 5514:Trefftz method 5511: 5505: 5504: 5503: 5498: 5492: 5486: 5477: 5471: 5465: 5459: 5458: 5457: 5445: 5427: 5424: 5423: 5422: 5421: 5420: 5414: 5406: 5401: 5387: 5386: 5385: 5379: 5378: 5377: 5366: 5360: 5354: 5345: 5344: 5343: 5337: 5328: 5327: 5326: 5320: 5314: 5313: 5312: 5295: 5294: 5293: 5287: 5286: 5285: 5279: 5267: 5247: 5244: 5236: 5233: 5232: 5231: 5225: 5219: 5218: 5217: 5208:Stiff equation 5205: 5204: 5203: 5202: 5201: 5186: 5185: 5184: 5181:Nyström method 5175: 5174: 5173: 5167: 5161: 5152: 5151: 5150: 5144: 5135: 5134: 5133: 5127: 5119: 5118: 5117: 5112: 5104: 5103: 5102: 5096: 5095: 5094: 5088: 5070: 5069: 5068: 5063: 5057: 5051: 5045: 5036: 5030: 5024: 5018: 5017: 5016: 5010: 4999: 4996: 4993: 4990: 4987: 4984: 4981: 4977: 4974: 4959: 4947: 4946: 4945: 4940: 4934: 4928: 4922: 4916: 4910: 4904: 4898: 4886: 4880: 4874: 4868: 4854: 4851: 4850: 4849: 4844: 4843: 4842: 4836: 4825: 4820: 4815: 4809: 4803: 4802: 4801: 4787: 4781: 4775: 4769: 4768: 4767: 4762: 4756: 4746: 4732: 4722: 4702: 4696: 4690: 4684: 4683: 4682: 4674:Simpson's rule 4671: 4665: 4651: 4648: 4647: 4646: 4641: 4640: 4639: 4633: 4627: 4614: 4610: 4606: 4603: 4598: 4594: 4590: 4587: 4584: 4581: 4576: 4572: 4568: 4565: 4562: 4559: 4554: 4550: 4546: 4543: 4540: 4537: 4534: 4531: 4528: 4525: 4511: 4499: 4498: 4497: 4492: 4490:Penalty method 4487: 4479: 4473: 4468: 4462: 4461: 4460: 4444: 4443: 4442: 4437: 4435:BRST algorithm 4426: 4425: 4424: 4423: 4422: 4417: 4415:Odds algorithm 4406: 4400: 4394: 4384: 4377: 4374: 4373: 4372: 4367: 4362: 4357: 4352: 4347: 4342: 4336: 4331: 4326: 4320: 4315: 4309: 4303: 4297: 4292: 4291: 4290: 4285: 4280: 4270: 4265: 4260: 4255: 4250: 4244: 4239: 4234: 4228: 4223: 4222: 4221: 4215: 4206: 4205: 4204: 4198: 4187: 4184: 4183: 4182: 4176: 4170: 4165: 4164: 4163: 4157: 4146: 4141: 4135: 4129: 4128: 4127: 4126: 4125: 4119: 4095: 4090: 4089: 4088: 4078: 4077: 4076: 4064: 4059: 4058: 4057: 4051: 4045: 4039: 4033: 4027: 4021: 4016: 4011: 4008:Strong duality 4005: 3994: 3993: 3992: 3986: 3981: 3935: 3918:) ≄ 0 implies 3845: 3842: 3841: 3840: 3839: 3838: 3832: 3829:Harmony search 3826: 3821: 3816: 3811: 3810: 3809: 3803: 3797: 3796: 3795: 3781: 3776: 3766: 3760: 3759: 3758: 3752: 3747: 3736: 3724: 3723: 3722: 3717: 3712: 3707: 3702: 3696: 3695: 3694: 3684: 3679: 3669: 3666: 3665: 3664: 3658: 3657: 3656: 3640: 3628: 3627: 3621: 3615: 3609: 3608: 3607: 3601: 3595: 3589: 3583: 3577: 3571: 3560: 3554: 3548: 3542: 3537: 3531: 3525: 3524: 3523: 3522: 3521: 3509: 3500: 3499: 3498: 3492: 3473: 3470: 3469: 3468: 3467: 3466: 3460: 3455: 3454: 3453: 3452: 3451: 3436: 3430: 3427: 3421: 3416: 3414:Ternary search 3411: 3405: 3404: 3403: 3397: 3391: 3386: 3381: 3380: 3379: 3373: 3358: 3353: 3352: 3351: 3333: 3327: 3321: 3320: 3319: 3313: 3312: 3311: 3295: 3294: 3293: 3292: 3291: 3286: 3276: 3270: 3259: 3258: 3257: 3256: 3255: 3249: 3241: 3235: 3234: 3233: 3232: 3231: 3219: 3213: 3208: 3207: 3206: 3200: 3197:BHHH algorithm 3189: 3178: 3145: 3144: 3143: 3131: 3126: 3125: 3124: 3118: 3106: 3084: 3081: 3080: 3079: 3073: 3067: 3061: 3058:Bregman method 3055: 3054: 3053: 3050: 3045: 3040: 3030: 3025: 3024: 3023: 3022: 3021: 3005: 2999: 2998: 2997: 2992: 2986: 2981: 2976: 2959: 2956: 2955: 2954: 2948: 2943: 2938: 2932: 2927: 2921: 2920: 2919: 2914: 2909: 2904: 2896: 2891: 2890: 2889: 2883: 2878: 2877: 2876: 2871: 2866: 2856: 2855: 2854: 2848: 2842: 2836: 2810: 2807: 2806: 2805: 2800: 2795: 2793:Slack variable 2790: 2785: 2779:Global optimum 2776: 2770: 2765: 2764: 2763: 2757: 2746: 2741: 2734: 2733:Basic concepts 2731: 2723: 2720: 2719: 2718: 2717: 2716: 2705: 2704: 2703: 2695: 2694: 2693: 2688: 2683: 2677: 2672: 2667: 2662: 2654: 2653: 2652: 2638: 2620: 2614: 2611:Brent's method 2608: 2602: 2596: 2590: 2584: 2578: 2577: 2576: 2570: 2569: 2568: 2562: 2556: 2550: 2544: 2532: 2529:Newton fractal 2526: 2514: 2509: 2508: 2507: 2477: 2476: 2465: 2462: 2461: 2460: 2455: 2450: 2449: 2448: 2438: 2432: 2431: 2430: 2417: 2414: 2413: 2412: 2411: 2410: 2405: 2397: 2392: 2386: 2380: 2374: 2367:Fekete problem 2364: 2358: 2352: 2346: 2345: 2344: 2338: 2332: 2327: 2317: 2311: 2310: 2309: 2298: 2290: 2289: 2288: 2282: 2276: 2275: 2274: 2259: 2258: 2257: 2251: 2245: 2239: 2233: 2227: 2221: 2215: 2205: 2199: 2191: 2185: 2179: 2178: 2177: 2165: 2159: 2153: 2152: 2151: 2141: 2136: 2124: 2121: 2120: 2119: 2118: 2117: 2111: 2105: 2099: 2094: 2089: 2084: 2078: 2072: 2060: 2059: 2058: 2046: 2041: 2040: 2039: 2030: 2029: 2028: 2023: 2018: 2007: 2006: 2005: 2000: 1987: 1977: 1956: 1951: 1950: 1949: 1939: 1934: 1924: 1923: 1922: 1909: 1906: 1905: 1904: 1899: 1893: 1888: 1887: 1886: 1885: 1884: 1879: 1871: 1865: 1862:Twiddle factor 1859: 1854: 1848: 1843: 1838: 1833: 1827: 1822: 1817: 1806: 1805: 1804: 1785: 1782: 1781: 1780: 1774: 1768: 1762: 1756: 1750: 1744: 1739: 1738: 1737: 1725: 1724: 1723: 1717: 1712: 1701: 1700: 1699: 1698: 1697: 1691:BĂ©zier surface 1688: 1676: 1671: 1661: 1659:Hermite spline 1656: 1651: 1650: 1649: 1638: 1627:Perfect spline 1624: 1610: 1607: 1606: 1605: 1600: 1595: 1590: 1589: 1588: 1578: 1573: 1568: 1563: 1555: 1554: 1553: 1547: 1541: 1536: 1535: 1534: 1528: 1515: 1510: 1505: 1500: 1495: 1490: 1477: 1474: 1473: 1472: 1458: 1455: 1454: 1453: 1447: 1441: 1435: 1429: 1424: 1419: 1414: 1413: 1412: 1407: 1406: 1405: 1394: 1381: 1378: 1377: 1376: 1370: 1364: 1359: 1354: 1353: 1352: 1347: 1335: 1330: 1329: 1328: 1316: 1310: 1305: 1300: 1287: 1284: 1283: 1282: 1281: 1280: 1274: 1268: 1259: 1258: 1257: 1251: 1250: 1249: 1243: 1235:Preconditioner 1232: 1227: 1224:Stone's method 1221: 1215: 1209: 1203: 1202: 1201: 1189: 1188: 1187: 1181: 1170: 1165: 1164: 1163: 1157: 1156: 1155: 1138: 1130: 1124: 1118: 1112: 1111: 1110: 1104: 1101:Frontal solver 1095: 1089: 1088: 1087: 1082: 1071: 1066: 1065: 1064: 1058: 1047: 1046: 1045: 1039: 1033: 1020: 1017: 1016: 1015: 1009: 1008: 1007: 1001: 1000: 999: 993: 987: 986: 985: 973: 964: 958: 957: 956: 944: 932: 931: 930: 924: 918: 913: 905: 904: 903: 897: 891: 888:Hilbert matrix 885: 879: 873: 868: 863: 858: 857: 856: 854:Skyline matrix 851: 846: 841: 836: 821: 820:Basic concepts 818: 810: 807: 806: 805: 804: 803: 798: 792: 786: 780: 774: 768: 762: 759:Wallis product 756: 750: 735: 729: 723: 713: 707: 706: 705: 699: 691: 690: 689: 683: 677: 668: 667: 666: 651: 645: 631: 623: 618: 610: 609: 608: 603: 598: 592: 584: 583: 582: 571: 570: 569: 564: 556: 555: 554: 549: 535: 530: 525: 520: 509: 508: 507: 501: 495: 489: 483: 474: 473: 472: 467: 462: 456: 448: 441: 438: 437: 436: 431: 426: 420: 418:Sterbenz lemma 415: 414: 413: 407: 396: 366: 365: 364: 359: 351: 346: 341: 336: 335: 334: 333: 332: 316: 304: 303: 302: 297: 296: 295: 285: 279: 270:Floating point 267: 262: 257: 252: 247: 235: 232: 231: 230: 229: 228: 223: 206: 205: 204: 193: 184: 183: 182: 177: 172: 169:Nick Trefethen 162: 154: 148: 147: 146: 140: 132: 127: 125:Discretization 122: 117: 111: 106: 105: 104: 92: 91: 90: 84: 78: 73: 67: 55: 54: 53: 41: 36: 29: 26: 13: 10: 9: 6: 4: 3: 2: 7112: 7101: 7098: 7096: 7093: 7091: 7088: 7086: 7083: 7081: 7078: 7077: 7075: 7061: 7059:9780199233007 7055: 7051: 7047: 7043: 7036: 7033: 7026: 7022: 7019: 7017: 7014: 7012: 7009: 7007: 7004: 7002: 6999: 6997: 6994: 6992: 6989: 6987: 6984: 6982: 6981:Gene H. Golub 6979: 6977: 6974: 6973: 6969: 6963: 6960: 6958: 6955: 6954: 6953: 6949: 6947: 6944: 6942: 6939: 6937: 6934: 6931: 6927: 6924: 6922: 6921:Acta Numerica 6919: 6918: 6914: 6912: 6910: 6902: 6898: 6895: 6893: 6890: 6885: 6882: 6880: 6877: 6875: 6872: 6870: 6867: 6866: 6865: 6862: 6857: 6854: 6851: 6848: 6844: 6841: 6840: 6839: 6836: 6832: 6831:Geodesic grid 6829: 6828: 6827: 6824: 6822: 6821:Climate model 6819: 6816: 6813: 6809: 6806: 6803: 6800: 6797: 6794: 6792: 6789: 6787: 6784: 6782: 6779: 6778: 6776: 6773: 6771: 6768: 6767: 6766: 6763: 6762: 6758: 6754: 6751:Also see the 6750: 6745: 6742: 6739: 6736: 6732: 6729: 6726: 6723: 6720: 6717: 6716: 6714: 6710: 6707: 6705: 6702: 6700: 6697: 6695: 6692: 6689: 6686: 6685: 6684: 6681: 6676: 6673: 6672: 6671: 6668: 6664: 6661: 6659: 6656: 6655: 6654: 6651: 6649: 6646: 6644: 6641: 6638: 6635: 6633: 6630: 6628: 6625: 6622: 6619: 6616: 6613: 6612: 6610: 6607: 6604: 6602: 6599: 6596: 6593: 6591: 6588: 6585: 6582: 6580: 6577: 6575: 6572: 6568: 6565: 6564: 6563: 6560: 6556: 6553: 6551: 6548: 6546: 6543: 6541: 6538: 6536: 6533: 6532: 6530: 6527: 6523: 6520: 6517: 6514: 6510: 6507: 6505: 6502: 6501: 6499: 6494: 6491: 6490: 6488: 6485: 6482: 6479: 6478: 6477: 6474: 6470: 6467: 6465: 6462: 6458: 6455: 6454: 6453: 6450: 6446: 6443: 6441: 6438: 6437: 6436: 6433: 6429: 6426: 6424: 6421: 6419: 6416: 6411: 6408: 6405: 6402: 6399: 6396: 6393: 6390: 6389: 6388: 6385: 6384: 6383: 6380: 6378: 6375: 6373: 6370: 6369: 6367: 6366: 6363: 6360: 6355: 6352: 6349: 6346: 6343: 6340: 6337: 6334: 6331: 6328: 6326: 6323: 6319: 6316: 6315: 6313: 6310: 6307: 6304: 6301: 6298: 6295: 6292: 6291: 6287: 6282: 6279: 6276: 6273: 6270: 6267: 6264: 6261: 6256: 6253: 6250: 6247: 6246: 6244: 6241: 6238: 6235: 6232: 6230:Subdivisions: 6229: 6224: 6221: 6219: 6216: 6213: 6210: 6207: 6204: 6203: 6202: 6199: 6194: 6193:Geodesic grid 6191: 6189: 6186: 6183: 6180: 6177: 6174: 6169: 6166: 6164: 6161: 6158: 6155: 6152: 6149: 6146: 6143: 6140: 6137: 6134: 6131: 6128: 6125: 6122: 6119: 6116: 6113: 6110: 6107: 6106: 6104: 6103:Triangle mesh 6101: 6098: 6095: 6094: 6092: 6091:Types of mesh 6088: 6085: 6084: 6080: 6075: 6072: 6069: 6066: 6063: 6060: 6057: 6054: 6049: 6046: 6043: 6040: 6037: 6034: 6031: 6028: 6025: 6022: 6019: 6016: 6013: 6010: 6007: 6004: 6001: 5998: 5995: 5992: 5989: 5986: 5983: 5980: 5978: 5975: 5974: 5972: 5969: 5966: 5963: 5962: 5958: 5953: 5950: 5947: 5944: 5939: 5936: 5933: 5930: 5927: 5924: 5923: 5921: 5918: 5915: 5912: 5909: 5906: 5903: 5901: 5898: 5896: 5893: 5891: 5888: 5885: 5882: 5880: 5877: 5875: 5872: 5867: 5864: 5863: 5861: 5858: 5853: 5850: 5847: 5844: 5841: 5838: 5835: 5832: 5831: 5829: 5822: 5819: 5816: 5813: 5810: 5807: 5804: 5801: 5800: 5798: 5795: 5792: 5790: 5787: 5784: 5781: 5779: 5776: 5773: 5770: 5769: 5767: 5764: 5759: 5756: 5753: 5750: 5749: 5747: 5744: 5739: 5736: 5733: 5730: 5727: 5724: 5721: 5718: 5715: 5712: 5709: 5706: 5705: 5703: 5700: 5697: 5694: 5689: 5686: 5685: 5683: 5680: 5677: 5674: 5670: 5667: 5666: 5664: 5661: 5660: 5657:Other methods 5656: 5652: 5649: 5647: 5644: 5640: 5637: 5634: 5631: 5628: 5625: 5624: 5622: 5619: 5616: 5614: 5611: 5608: 5605: 5602: 5599: 5596: 5593: 5591: 5588: 5585: 5582: 5579: 5576: 5573: 5570: 5567: 5564: 5561: 5558: 5555: 5552: 5549: 5546: 5543: 5540: 5537: 5534: 5531: 5528: 5525: 5522: 5520: 5517: 5515: 5512: 5509: 5506: 5502: 5499: 5496: 5493: 5490: 5487: 5484: 5481: 5480: 5478: 5475: 5472: 5469: 5466: 5463: 5460: 5455: 5452: 5451: 5449: 5446: 5443: 5440: 5439: 5438: 5436: 5432: 5425: 5418: 5415: 5413: 5410: 5409: 5407: 5405: 5402: 5399: 5395: 5391: 5388: 5383: 5380: 5375: 5372: 5371: 5370: 5369:Upwind scheme 5367: 5364: 5361: 5358: 5355: 5352: 5349: 5348: 5346: 5341: 5338: 5335: 5332: 5331: 5329: 5324: 5321: 5318: 5315: 5311: 5308: 5307: 5305: 5302: 5301: 5299: 5296: 5291: 5288: 5283: 5280: 5277: 5274: 5273: 5271: 5268: 5265: 5262: 5261: 5259: 5256: 5255: 5254: 5252: 5245: 5243: 5241: 5234: 5229: 5226: 5223: 5220: 5215: 5212: 5211: 5209: 5206: 5199: 5196: 5195: 5193: 5190: 5189: 5187: 5182: 5179: 5178: 5176: 5171: 5168: 5165: 5162: 5159: 5156: 5155: 5153: 5148: 5145: 5142: 5139: 5138: 5136: 5131: 5128: 5126: 5123: 5122: 5120: 5116: 5113: 5111: 5108: 5107: 5105: 5100: 5097: 5092: 5089: 5086: 5083: 5082: 5080: 5077: 5076: 5074: 5071: 5067: 5064: 5061: 5058: 5055: 5052: 5049: 5046: 5043: 5040: 5039: 5037: 5034: 5031: 5028: 5025: 5022: 5019: 5014: 5011: 4994: 4991: 4988: 4982: 4979: 4975: 4972: 4963: 4960: 4957: 4954: 4953: 4951: 4948: 4944: 4941: 4938: 4937:Butcher group 4935: 4932: 4929: 4926: 4923: 4920: 4917: 4914: 4911: 4908: 4905: 4902: 4901:Heun's method 4899: 4896: 4893: 4892: 4890: 4887: 4884: 4881: 4878: 4875: 4872: 4869: 4866: 4863: 4862: 4861: 4859: 4852: 4848: 4845: 4840: 4837: 4835: 4832: 4831: 4829: 4826: 4824: 4821: 4819: 4816: 4813: 4810: 4807: 4804: 4800: 4799: 4794: 4793: 4791: 4788: 4785: 4782: 4779: 4776: 4773: 4770: 4766: 4763: 4760: 4757: 4754: 4750: 4747: 4744: 4740: 4736: 4733: 4730: 4726: 4723: 4718: 4712: 4709: 4708: 4706: 4703: 4700: 4697: 4694: 4691: 4688: 4685: 4681: 4678: 4677: 4675: 4672: 4669: 4666: 4663: 4660: 4659: 4658: 4656: 4649: 4645: 4642: 4637: 4634: 4631: 4628: 4612: 4604: 4601: 4596: 4592: 4588: 4585: 4579: 4574: 4566: 4563: 4560: 4557: 4552: 4548: 4541: 4535: 4532: 4529: 4523: 4515: 4512: 4509: 4506: 4505: 4503: 4500: 4496: 4493: 4491: 4488: 4486: 4483: 4482: 4480: 4477: 4474: 4472: 4469: 4466: 4463: 4458: 4455:— for linear 4454: 4451: 4450: 4448: 4445: 4441: 4440:MCS algorithm 4438: 4436: 4433: 4432: 4430: 4427: 4421: 4418: 4416: 4413: 4412: 4410: 4407: 4404: 4401: 4398: 4395: 4393: 4390: 4389: 4388: 4385: 4383: 4380: 4379: 4376:Miscellaneous 4375: 4371: 4368: 4366: 4363: 4361: 4358: 4356: 4353: 4351: 4348: 4346: 4343: 4340: 4337: 4335: 4332: 4330: 4327: 4324: 4321: 4319: 4316: 4313: 4310: 4307: 4304: 4301: 4298: 4296: 4293: 4289: 4286: 4284: 4281: 4279: 4276: 4275: 4274: 4271: 4269: 4266: 4264: 4261: 4259: 4256: 4254: 4251: 4248: 4245: 4243: 4240: 4238: 4235: 4232: 4229: 4227: 4224: 4219: 4216: 4213: 4210: 4209: 4207: 4202: 4199: 4196: 4193: 4192: 4191:In geometry: 4190: 4189: 4185: 4180: 4177: 4174: 4171: 4169: 4166: 4161: 4158: 4156: 4153: 4152: 4150: 4147: 4145: 4142: 4139: 4136: 4133: 4130: 4123: 4120: 4118: 4115: 4114: 4113: 4110: 4109: 4108:⟩ = 0 4107: 4103: 4099: 4096: 4094: 4091: 4087: 4084: 4083: 4082: 4079: 4074: 4071: 4070: 4068: 4065: 4063: 4062:Farkas' lemma 4060: 4055: 4054:Wolfe duality 4052: 4049: 4046: 4043: 4040: 4037: 4034: 4031: 4028: 4025: 4022: 4020: 4017: 4015: 4012: 4009: 4006: 4003: 4000: 3999: 3998: 3995: 3990: 3987: 3985: 3984:Subderivative 3982: 3979: 3975: 3971: 3967: 3963: 3959: 3955: 3951: 3947: 3943: 3939: 3936: 3933: 3929: 3925: 3921: 3917: 3913: 3909: 3905: 3901: 3898: 3897: 3895: 3891: 3887: 3883: 3879: 3875: 3871: 3867: 3863: 3859: 3855: 3851: 3848: 3847: 3843: 3837: 3833: 3830: 3827: 3825: 3822: 3820: 3817: 3815: 3812: 3807: 3804: 3801: 3798: 3794: 3791: 3790: 3789: 3785: 3782: 3780: 3777: 3775: 3772: 3771: 3770: 3767: 3764: 3761: 3756: 3753: 3751: 3748: 3745: 3742: 3741: 3740: 3737: 3734: 3733:Random search 3731: 3730: 3728: 3725: 3721: 3718: 3716: 3713: 3711: 3708: 3706: 3703: 3700: 3697: 3693: 3690: 3689: 3688: 3685: 3683: 3680: 3678: 3675: 3674: 3672: 3671: 3667: 3662: 3659: 3654: 3651: 3650: 3648: 3644: 3641: 3638: 3635: 3634: 3633: 3632: 3625: 3622: 3619: 3618:Ross' π lemma 3616: 3613: 3610: 3605: 3602: 3599: 3596: 3593: 3590: 3587: 3584: 3581: 3578: 3575: 3572: 3569: 3566: 3565: 3564: 3561: 3558: 3555: 3552: 3549: 3546: 3543: 3541: 3538: 3535: 3532: 3529: 3526: 3519: 3516: 3515: 3513: 3510: 3507: 3504: 3503: 3501: 3496: 3493: 3490: 3487: 3486: 3484: 3481: 3480: 3479: 3478: 3471: 3464: 3463:Space mapping 3461: 3459: 3456: 3450: 3447: 3446: 3445: 3442: 3441: 3440: 3437: 3434: 3431: 3428: 3425: 3422: 3420: 3417: 3415: 3412: 3409: 3406: 3401: 3398: 3395: 3392: 3390: 3387: 3385: 3382: 3377: 3374: 3371: 3368: 3367: 3365: 3362: 3361: 3359: 3357: 3354: 3350: 3349: 3343: 3339: 3338: 3337: 3334: 3331: 3328: 3325: 3322: 3317: 3314: 3310: 3307: 3306: 3305: 3302: 3301: 3299: 3296: 3290: 3287: 3285: 3282: 3281: 3280: 3277: 3274: 3271: 3269: 3266: 3265: 3263: 3262: 3260: 3253: 3250: 3248: 3245: 3244: 3242: 3239: 3236: 3229: 3226: 3225: 3223: 3220: 3217: 3214: 3212: 3209: 3204: 3201: 3198: 3195: 3194: 3193: 3190: 3188: 3185: 3184: 3182: 3181:Least squares 3179: 3176: 3172: 3169: 3165: 3161: 3157: 3153: 3150:(NCP) — find 3149: 3146: 3141: 3138: 3137: 3135: 3132: 3130: 3127: 3122: 3119: 3116: 3113: 3112: 3110: 3107: 3104: 3100: 3096: 3095: 3093: 3092: 3091: 3089: 3082: 3077: 3074: 3071: 3068: 3065: 3062: 3059: 3056: 3051: 3049: 3046: 3044: 3041: 3039: 3036: 3035: 3034: 3031: 3029: 3026: 3019: 3016: 3015: 3013: 3010: 3009: 3003: 3002:Basis pursuit 3000: 2996: 2993: 2990: 2987: 2985: 2982: 2980: 2977: 2975: 2972: 2971: 2970: 2967: 2966: 2965: 2964: 2957: 2952: 2949: 2947: 2944: 2942: 2939: 2936: 2933: 2931: 2928: 2925: 2922: 2918: 2915: 2913: 2910: 2908: 2905: 2903: 2900: 2899: 2897: 2895: 2892: 2887: 2884: 2882: 2879: 2875: 2872: 2870: 2867: 2865: 2862: 2861: 2860: 2857: 2852: 2849: 2846: 2843: 2840: 2837: 2834: 2831: 2830: 2829: 2826: 2825: 2823: 2822: 2821: 2819: 2816:(also treats 2815: 2808: 2804: 2801: 2799: 2796: 2794: 2791: 2789: 2786: 2784: 2783:Local optimum 2780: 2777: 2774: 2771: 2769: 2766: 2761: 2758: 2755: 2752: 2751: 2750: 2747: 2745: 2742: 2740: 2737: 2736: 2732: 2730: 2728: 2721: 2715: 2712: 2711: 2709: 2706: 2702: 2699: 2698: 2696: 2692: 2689: 2687: 2684: 2681: 2678: 2676: 2673: 2671: 2668: 2666: 2663: 2661: 2660:Aberth method 2658: 2657: 2655: 2650: 2646: 2643:— uses first 2642: 2639: 2636: 2632: 2628: 2624: 2621: 2618: 2615: 2612: 2609: 2606: 2603: 2600: 2597: 2594: 2591: 2588: 2585: 2582: 2581:Secant method 2579: 2574: 2571: 2566: 2563: 2560: 2557: 2554: 2551: 2548: 2545: 2542: 2539: 2538: 2536: 2533: 2530: 2527: 2524: 2521: 2520: 2518: 2515: 2513: 2510: 2505: 2502: 2501: 2499: 2496: 2495: 2493: 2492: 2491: 2489: 2485: 2481: 2475: 2473: 2468: 2467: 2463: 2459: 2456: 2454: 2451: 2447: 2444: 2443: 2442: 2439: 2436: 2433: 2428: 2425: 2424: 2423: 2422:Extrapolation 2420: 2419: 2416:Miscellaneous 2415: 2409: 2406: 2404: 2401: 2400: 2398: 2396: 2393: 2390: 2387: 2384: 2381: 2378: 2375: 2372: 2368: 2365: 2362: 2359: 2356: 2353: 2350: 2347: 2342: 2339: 2336: 2333: 2331: 2328: 2325: 2321: 2318: 2315: 2312: 2307: 2304: 2303: 2302: 2299: 2297: 2294: 2293: 2291: 2286: 2283: 2280: 2277: 2272: 2269: 2268: 2266: 2263: 2262: 2260: 2255: 2252: 2249: 2246: 2243: 2240: 2237: 2234: 2231: 2228: 2225: 2222: 2219: 2216: 2213: 2209: 2206: 2203: 2200: 2198: 2195: 2194: 2192: 2189: 2186: 2183: 2180: 2175: 2172: 2171: 2169: 2166: 2163: 2160: 2157: 2154: 2150: 2147: 2146: 2145: 2144:Curve fitting 2142: 2140: 2137: 2135: 2132: 2131: 2130: 2129: 2122: 2116: 2112: 2109: 2106: 2103: 2100: 2098: 2095: 2093: 2090: 2088: 2085: 2082: 2079: 2076: 2075:Coons surface 2073: 2070: 2067: 2066: 2064: 2061: 2056: 2053: 2052: 2050: 2047: 2045: 2042: 2037: 2036: 2034: 2031: 2027: 2024: 2022: 2019: 2017: 2014: 2013: 2011: 2008: 2004: 2001: 1999: 1995: 1991: 1988: 1985: 1982: 1981: 1976: 1972: 1968: 1964: 1960: 1957: 1955: 1952: 1948: 1944: 1940: 1938: 1935: 1933: 1930: 1929: 1928: 1925: 1920: 1917: 1916: 1915: 1912: 1911: 1907: 1903: 1900: 1897: 1894: 1892: 1889: 1883: 1880: 1878: 1875: 1874: 1872: 1869: 1866: 1863: 1860: 1858: 1855: 1852: 1849: 1847: 1844: 1842: 1839: 1837: 1834: 1831: 1828: 1826: 1823: 1821: 1818: 1816: 1813: 1812: 1810: 1807: 1803: 1800: 1799: 1797: 1794: 1793: 1792: 1790: 1783: 1779: 1775: 1772: 1769: 1766: 1763: 1760: 1757: 1754: 1751: 1748: 1745: 1743: 1740: 1735: 1732: 1731: 1729: 1726: 1721: 1718: 1716: 1713: 1710: 1707: 1706: 1705: 1702: 1696: 1692: 1689: 1687: 1683: 1680: 1679: 1677: 1675: 1672: 1670: 1667: 1666: 1665: 1662: 1660: 1657: 1655: 1652: 1647: 1644: 1643: 1642: 1639: 1636: 1632: 1628: 1625: 1622: 1619: 1618: 1617: 1615: 1608: 1604: 1601: 1599: 1596: 1594: 1591: 1586: 1582: 1579: 1577: 1574: 1572: 1569: 1567: 1564: 1562: 1559: 1558: 1556: 1551: 1548: 1545: 1542: 1540: 1537: 1532: 1529: 1527: 1524: 1523: 1522: 1519: 1518: 1516: 1514: 1511: 1509: 1506: 1504: 1501: 1499: 1496: 1494: 1491: 1489: 1486: 1485: 1484: 1482: 1475: 1470: 1467: 1466: 1465: 1463: 1462:Interpolation 1456: 1451: 1448: 1445: 1444:Pivot element 1442: 1439: 1436: 1433: 1430: 1428: 1425: 1423: 1420: 1418: 1415: 1411: 1408: 1403: 1400: 1399: 1398: 1395: 1393: 1390: 1389: 1387: 1384: 1383: 1379: 1374: 1371: 1368: 1365: 1363: 1360: 1358: 1355: 1351: 1348: 1345: 1342: 1341: 1339: 1336: 1334: 1331: 1326: 1323: 1322: 1320: 1317: 1314: 1311: 1309: 1306: 1304: 1301: 1299: 1296: 1295: 1294: 1292: 1285: 1278: 1275: 1272: 1269: 1266: 1263: 1262: 1260: 1255: 1252: 1247: 1244: 1241: 1238: 1237: 1236: 1233: 1231: 1228: 1225: 1222: 1219: 1216: 1213: 1210: 1207: 1204: 1199: 1196: 1195: 1193: 1190: 1185: 1182: 1180: 1177: 1176: 1174: 1171: 1169: 1166: 1161: 1158: 1153: 1150: 1149: 1147: 1144: 1143: 1142: 1139: 1137: 1136:Jacobi method 1134: 1133: 1131: 1128: 1125: 1122: 1119: 1116: 1113: 1108: 1105: 1102: 1099: 1098: 1096: 1093: 1090: 1086: 1083: 1081: 1078: 1077: 1075: 1072: 1070: 1067: 1062: 1059: 1057: 1054: 1053: 1051: 1048: 1043: 1040: 1037: 1034: 1031: 1028: 1027: 1026: 1023: 1022: 1018: 1013: 1010: 1005: 1002: 997: 994: 991: 988: 983: 980: 979: 977: 974: 971: 968: 967: 965: 962: 959: 954: 951: 950: 948: 945: 942: 939: 938: 936: 933: 928: 925: 922: 919: 917: 914: 912: 909: 908: 906: 901: 898: 895: 892: 889: 886: 883: 880: 877: 874: 872: 869: 867: 864: 862: 859: 855: 852: 850: 847: 845: 842: 840: 837: 835: 832: 831: 830: 829:Sparse matrix 827: 826: 824: 823: 819: 817: 815: 808: 802: 799: 796: 793: 790: 787: 784: 781: 778: 775: 772: 769: 766: 763: 760: 757: 754: 751: 748: 745: 744: 742: 736: 733: 730: 727: 724: 721: 717: 714: 711: 708: 703: 700: 698: 695: 694: 692: 687: 686:BKM algorithm 684: 681: 678: 675: 672: 671: 669: 662: 655: 652: 649: 646: 643: 639: 635: 632: 630: 628: 624: 622: 619: 617: 614: 613: 611: 607: 604: 602: 599: 596: 593: 591: 588: 587: 586:Polynomials: 585: 581: 578: 577: 575: 572: 568: 565: 563: 560: 559: 557: 553: 550: 547: 543: 539: 536: 534: 531: 529: 526: 524: 521: 519: 518:Long division 516: 515: 513: 510: 505: 502: 499: 496: 493: 490: 487: 484: 481: 478: 477: 475: 471: 468: 466: 463: 460: 457: 455: 452: 451: 449: 447: 444: 443: 439: 435: 432: 430: 427: 424: 421: 419: 416: 411: 408: 405: 402: 401: 400: 397: 394: 390: 386: 382: 378: 374: 370: 367: 363: 360: 358: 355: 354: 352: 350: 347: 345: 342: 340: 337: 331: 327: 323: 322: 320: 317: 314: 311: 310: 308: 305: 301: 298: 294: 291: 290: 289: 286: 283: 280: 277: 274: 273: 271: 268: 266: 263: 261: 258: 256: 253: 251: 248: 246: 245:Approximation 243: 242: 241: 240: 233: 227: 224: 222: 218: 214: 210: 207: 202: 199: 198: 197: 194: 191: 188: 187: 185: 181: 178: 176: 173: 170: 166: 163: 161: 158: 157: 155: 152: 149: 144: 141: 139: 136: 135: 133: 131: 128: 126: 123: 121: 118: 115: 112: 110: 107: 102: 99: 98: 96: 93: 88: 85: 82: 79: 77: 74: 71: 68: 65: 62: 61: 59: 56: 51: 48: 47: 45: 42: 40: 37: 35: 32: 31: 27: 25: 23: 21: 7041: 7035: 6906: 6759:Applications 6531:techniques: 6182:Regular grid 6097:Polygon mesh 6056:Coarse space 5932:Multiphysics 5726:Flux limiter 5714:MUSCL scheme 5536:Superelement 5429: 5397: 5393: 5249: 5238: 5099:Energy drift 4865:Euler method 4856: 4795: 4752: 4742: 4738: 4728: 4716: 4687:Boole's rule 4653: 4495:Trust region 4345:Stigler diet 4186:Applications 4173:Reduced cost 4105: 4101: 4014:Shadow price 4002:Weak duality 3977: 3973: 3969: 3965: 3961: 3957: 3953: 3949: 3945: 3941: 3931: 3927: 3923: 3919: 3915: 3911: 3907: 3903: 3893: 3889: 3885: 3881: 3877: 3873: 3869: 3865: 3861: 3857: 3853: 3835: 3814:Luus–Jaakola 3729:algorithms: 3629: 3475: 3433:MM algorithm 3347: 3341: 3174: 3170: 3167: 3163: 3159: 3155: 3151: 3102: 3098: 3086: 3004:— minimize L 2961: 2851:Big M method 2833:Bland's rule 2817: 2812: 2725: 2722:Optimization 2648: 2644: 2634: 2630: 2626: 2487: 2483: 2478: 2469: 2370: 2323: 2211: 2126: 2114: 1997: 1993: 1974: 1970: 1966: 1962: 1787: 1694: 1685: 1664:BĂ©zier curve 1634: 1630: 1612: 1584: 1581:Padua points 1479: 1460: 1388:algorithms: 1333:QR algorithm 1289: 1061:LU reduction 876:Block matrix 812: 720:power series 660: 641: 637: 626: 544:to find the 533:SRT division 392: 388: 384: 380: 376: 372: 237: 220: 216: 212: 134:Complexity: 17: 15: 6976:Cleve Moler 6970:Researchers 6176:Volume mesh 5560:CĂ©a's lemma 5334:FTCS scheme 5214:L-stability 4818:Sparse grid 4024:Duality gap 3940:— function 3906:such that ∇ 3902:— function 3852:— function 3624:Sethi model 3419:Tabu search 3279:Line search 3273:Guess value 2097:PDE surface 2055:Pick matrix 1747:Coons patch 834:Band matrix 450:Summation: 276:Guard digit 226:ABS methods 7074:Categories 7027:References 6869:Cell lists 5911:Roe solver 5400:-direction 5188:Analysis: 3944:such that 3856:such that 3551:DNSS point 3264:Concepts: 3166:) ≄ 0 and 3154:such that 3121:Posynomial 2739:Active set 2697:Analysis: 2399:Journals: 2306:PadĂ© table 1941:See also: 1776:See also: 1709:Box spline 716:FEE method 710:AGM method 546:reciprocal 324:See also: 282:Truncation 16:This is a 7006:Peter Lax 4796:See also 4602:− 4564:− 3880:) + (1 − 3115:Signomial 387:| / max(| 7095:Outlines 6915:Journals 6903:Software 6288:Analysis 5228:Parareal 4976:″ 4459:problems 3960:) ≀ max( 3346:section 1759:I-spline 1753:M-spline 1734:T-spline 1730:(NURBS) 1704:B-spline 215:) = sin( 18:list of 6006:FETI-DP 5633:G space 5572:MAFELAP 4741:) (1 + 3976:)) for 3952:+ (1 − 3864:+ (1 − 3344:in the 3230:(NIPLS) 2625:— uses 2369:— find 1927:Wavelet 1194:(BiCG) 658:√ 540:: uses 272:number 171:in 2002 28:General 7056:  6777:(CFD) 6002:(FETI) 5578:NAFEMS 5474:hp-FEM 3892:) for 3808:(SPSA) 3800:MCACEA 2633:' and 2490:) = 0 1633:whose 1367:LOBPCG 680:CORDIC 22:topics 5823:(SBM) 5817:(RMM) 5811:(BPM) 5805:(BKM) 4755:) on 4745:) on 4731:) on 4715:(1 − 3177:) = 0 3158:≄ 0, 3105:above 2033:Slerp 722:for e 634:hypot 234:Error 7054:ISBN 6884:DIIS 5720:AUSM 3926:) ≄ 3872:) ≄ 3101:and 3097:See 2781:and 2470:See 1996:log 1965:) = 470:2Sum 391:|, | 379:is | 375:and 219:) / 7046:doi 4721:on 3968:), 3910:· ( 3896:∈ 1980:|) 7076:: 7052:. 6911:. 6093:: 6089:/ 4567:11 4504:: 4431:: 4104:, 3980:∈ 3950:tx 3914:− 3874:tf 3862:tx 3786:, 3645:, 2629:, 1969:(| 1945:, 937:: 743:: 640:+ 395:|) 383:− 328:, 24:. 7062:. 7048:: 6932:) 5398:y 5394:x 4998:) 4995:y 4992:, 4989:t 4986:( 4983:f 4980:= 4973:y 4753:x 4743:x 4739:x 4729:x 4719:) 4717:x 4613:2 4609:) 4605:7 4597:2 4593:y 4589:+ 4586:x 4583:( 4580:+ 4575:2 4571:) 4561:y 4558:+ 4553:2 4549:x 4545:( 4542:= 4539:) 4536:y 4533:, 4530:x 4527:( 4524:f 4106:v 4102:u 3978:t 3974:y 3972:( 3970:f 3966:x 3964:( 3962:f 3958:y 3956:) 3954:t 3948:( 3946:f 3942:f 3934:) 3932:x 3930:( 3928:f 3924:y 3922:( 3920:f 3916:x 3912:y 3908:f 3904:f 3894:t 3890:y 3888:( 3886:f 3884:) 3882:t 3878:x 3876:( 3870:y 3868:) 3866:t 3860:( 3858:f 3854:f 3175:x 3173:( 3171:f 3168:x 3164:x 3162:( 3160:f 3156:x 3152:x 3006:1 2649:d 2645:d 2635:f 2631:f 2627:f 2488:x 2486:( 2484:f 2371:N 2324:x 2212:x 1998:r 1994:r 1978:0 1975:x 1973:− 1971:x 1967:φ 1963:x 1695:R 1686:R 1635:m 1631:m 1585:R 740:π 661:x 644:) 642:y 638:x 627:n 393:y 389:x 385:y 381:x 377:y 373:x 221:x 217:x 213:x

Index

numerical analysis
Validated numerics
Iterative method
Rate of convergence
Order of accuracy
Series acceleration
Aitken's delta-squared process
Minimum polynomial extrapolation
Richardson extrapolation
Shanks transformation
Van Wijngaarden transformation
Abramowitz and Stegun
Digital Library of Mathematical Functions
Curse of dimensionality
Local convergence
Superconvergence
Discretization
Difference quotient
Computational complexity of mathematical operations
Smoothed analysis
Symbolic-numeric computation
History of numerical solution of differential equations using computers
Hundred-dollar, Hundred-digit Challenge problems
Nick Trefethen
International Workshops on Lattice QCD and Numerical Analysis
Timeline of numerical analysis after 1945
Collocation method
Level-set method
Level set (data structures)
Sinc numerical methods

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