Knowledge (XXG)

RRQR factorization

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can be used to generate an RRQR, but it is not an efficient method to do so. An RRQR implementation is available in MATLAB.
481: 445: 377: 273: 40: 227: 278: 192: 438: 237: 36: 232: 28: 211: 140: 122: 422: 361: 247: 114: 76: 32: 288: 418: 357: 206: 61: 465: 252: 349: 62:"Efficient algorithms for computing a strong rank-revealing QR factorization" 414: 268: 161: 406: 126: 103:"Rank-Revealing QR Factorizations and the Singular Value Decomposition" 319: 309: 118: 102: 80: 165: 426: 365: 297: 261: 220: 199: 446: 385: 177: 8: 60:Gu, Ming; Stanley C. Eisenstat (July 1996). 453: 439: 392: 378: 184: 170: 162: 315:Basic Linear Algebra Subprograms (BLAS) 52: 101:Hong, Y.P.; C.-T. Pan (January 1992). 7: 487:Algorithms and data structures stubs 403: 401: 346: 344: 69:SIAM Journal on Scientific Computing 35:which can be used to determine the 425:. You can help Knowledge (XXG) by 364:. You can help Knowledge (XXG) by 14: 405: 348: 25:rank-revealing QR factorization 1: 41:singular value decomposition 503: 400: 343: 228:System of linear equations 107:Mathematics of Computation 279:Cache-oblivious algorithm 16:Concept in linear algebra 477:Numerical linear algebra 330:General purpose software 193:Numerical linear algebra 31:algorithm based on the 421:-related article is a 360:-related article is a 472:Matrix decompositions 325:Specialized libraries 238:Matrix multiplication 233:Matrix decompositions 482:Linear algebra stubs 141:"RRQR Factorization" 29:matrix decomposition 212:Numerical stability 21:RRQR factorization 434: 433: 373: 372: 338: 337: 39:of a matrix. The 494: 455: 448: 441: 409: 402: 394: 387: 380: 352: 345: 248:Matrix splitting 186: 179: 172: 163: 156: 155: 153: 151: 145: 137: 131: 130: 113:(197): 213–232. 98: 92: 91: 89: 87: 66: 57: 33:QR factorization 502: 501: 497: 496: 495: 493: 492: 491: 462: 461: 460: 459: 419:data structures 399: 398: 341: 339: 334: 293: 289:Multiprocessing 257: 253:Sparse problems 216: 195: 190: 160: 159: 149: 147: 146:. 29 March 2007 143: 139: 138: 134: 119:10.2307/2153029 100: 99: 95: 85: 83: 81:10.1137/0917055 64: 59: 58: 54: 49: 17: 12: 11: 5: 500: 498: 490: 489: 484: 479: 474: 464: 463: 458: 457: 450: 443: 435: 432: 431: 410: 397: 396: 389: 382: 374: 371: 370: 358:linear algebra 353: 336: 335: 333: 332: 327: 322: 317: 312: 307: 301: 299: 295: 294: 292: 291: 286: 281: 276: 271: 265: 263: 259: 258: 256: 255: 250: 245: 235: 230: 224: 222: 218: 217: 215: 214: 209: 207:Floating point 203: 201: 197: 196: 191: 189: 188: 181: 174: 166: 158: 157: 132: 93: 75:(4): 848–869. 51: 50: 48: 45: 15: 13: 10: 9: 6: 4: 3: 2: 499: 488: 485: 483: 480: 478: 475: 473: 470: 469: 467: 456: 451: 449: 444: 442: 437: 436: 430: 428: 424: 420: 416: 411: 408: 404: 395: 390: 388: 383: 381: 376: 375: 369: 367: 363: 359: 354: 351: 347: 342: 331: 328: 326: 323: 321: 318: 316: 313: 311: 308: 306: 303: 302: 300: 296: 290: 287: 285: 282: 280: 277: 275: 272: 270: 267: 266: 264: 260: 254: 251: 249: 246: 243: 239: 236: 234: 231: 229: 226: 225: 223: 219: 213: 210: 208: 205: 204: 202: 198: 194: 187: 182: 180: 175: 173: 168: 167: 164: 142: 136: 133: 128: 124: 120: 116: 112: 108: 104: 97: 94: 82: 78: 74: 70: 63: 56: 53: 46: 44: 42: 38: 34: 30: 26: 22: 427:expanding it 412: 366:expanding it 355: 340: 200:Key concepts 148:. Retrieved 135: 110: 106: 96: 86:22 September 84:. Retrieved 72: 68: 55: 24: 20: 18: 466:Categories 415:algorithms 242:algorithms 47:References 269:CPU cache 298:Software 262:Hardware 221:Problems 150:2 April 127:2153029 320:LAPACK 310:MATLAB 125:  413:This 356:This 305:ATLAS 144:(PDF) 123:JSTOR 65:(PDF) 27:is a 423:stub 362:stub 284:SIMD 152:2011 88:2014 37:rank 417:or 274:TLB 115:doi 77:doi 23:or 19:An 468:: 121:. 111:58 109:. 105:. 73:17 71:. 67:. 454:e 447:t 440:v 429:. 393:e 386:t 379:v 368:. 244:) 240:( 185:e 178:t 171:v 154:. 129:. 117:: 90:. 79::

Index

matrix decomposition
QR factorization
rank
singular value decomposition
"Efficient algorithms for computing a strong rank-revealing QR factorization"
doi
10.1137/0917055
"Rank-Revealing QR Factorizations and the Singular Value Decomposition"
doi
10.2307/2153029
JSTOR
2153029
"RRQR Factorization"
v
t
e
Numerical linear algebra
Floating point
Numerical stability
System of linear equations
Matrix decompositions
Matrix multiplication
algorithms
Matrix splitting
Sparse problems
CPU cache
TLB
Cache-oblivious algorithm
SIMD
Multiprocessing

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