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with some c>0, where n is the number of nodes or bases used in the methods. However, Sugihara has recently found that the errors in the Sinc numerical methods based on double exponential transformation are
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with some k>0, in a setup that is also meaningful both theoretically and practically and are found to be best possible in a certain mathematical sense.
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Sinc approximation methods excel for problems whose solutions may have singularities, or infinite domains, or boundary layers.
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378:{\displaystyle C_{M,N}(f,h)(x)=\displaystyle \sum _{k=-M}^{N}f(kh)\,{\textrm {sinc}}\left({\dfrac {x}{h}}-k\right)}
158:{\displaystyle C(f,h)(x)=\sum _{k=-\infty }^{\infty }f(kh)\,{\textrm {sinc}}\left({\dfrac {x}{h}}-k\right)}
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Cardinal function C(f,h) which is an expansion of f defined by
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Indeed, Sinc are ubiquitous for approximating every operation of calculus
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The truncated Sinc expansion of f is defined by the following series:
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where the step size h>0 and where the sinc function is defined by
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In the standard setup of the sinc numerical methods, the errors (in
232:{\displaystyle {\textrm {sinc}}(x)={\frac {\sin(\pi x)}{\pi x}}}
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are numerical techniques for finding approximate solutions of
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approximate solution of initial and boundary value ordinary
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approximate solution of partial differential equations,
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Sinc
Methods for Quadrature and Differential Equations
568:{\displaystyle O\left(e^{-{\frac {kn}{\ln n}}}\right)}
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672:"Recent developments of the Sinc numerical methods"
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639:"Summary of sinc numerical methods"
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587:Handbook of Sinc Numerical Methods
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649:: 379–420.
439:convolution
427:transforms,
407:integration
400:derivatives
760:Categories
624:References
551:
534:−
485:−
364:−
311:−
301:∑
221:π
210:π
204:
145:−
100:∞
95:∞
92:−
82:∑
579:Reading
425:Laplace
421:Fourier
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593:
711:This
717:stub
610:ISBN
591:ISBN
423:and
342:sinc
181:sinc
123:sinc
38:sinc
32:and
20:and
680:doi
651:doi
647:121
201:sin
16:In
762::
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330:k
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281:h
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189:x
186:(
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148:k
139:h
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129:(
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114:h
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108:(
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89:=
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78:=
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72:x
69:(
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63:h
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54:(
51:C
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