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Lemm J.M., Meurant G. — Computer Solution of Large Linear Systems

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Название: Computer Solution of Large Linear Systems

Авторы: Lemm J.M., Meurant G.

Аннотация:

Hardbound. This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 777

Добавлена в каталог: 13.08.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Adjacency set      36 148 171
Algorithm complexity      62
Ancestor      139 172
Backward error      67 120 121 123 169 170
Backward error analysis      62 112 249
Band      140
Bandwidth      140 141 176 321 379
Bipartite graph      161 162
Bit reversal      182
BLAS      65 67
BLAS1      65 66
BLAS2      66
BLAS3      66 175
Block Cholesky factorization      111
Block cyclic distribution      127
Block diagonally dominant matrix      99
Block LU factorization      99 602
Block tridiagonal matrix      108—111 177 194 195 202 321 323 378 407 408 424 479 480 482 495 500 501 598 601 602 607 608 624 629 633
Block twisted factorization      109
Block UL factorization      602
Bordering algorithm      84 87
Cauchy — Schwarz inequality      3 6 516 517
Cayley — Hamilton theorem      337
Characteristic polynomial      244 509
Chebyshev polynomials      38 39 41 247 248 268 273 513 521 528 648
Cholesky factorization      94 100 104 105 149 283 284 293 300 304 466 480 502 531 649
Chord      37
CLIQUE      37 153 171 173 645 646
Complete pivoting      80 81 117
Componentwise condition number      120
Computer arithmetic      60
Computers      49 58 59 62—66 92 94 125 128 194 200 218 240 327 529 586 656
Condition number      120 170 242 246 250 268 271 274 275 284 311 335 397 399 400 402 403 405 409 410 423 427 436 445 446 448—450 452 469 475 478 493 494 511 513 517 531 583 586 602 604 614 618 621 623 624 631 632 641—643 646—648 653
Cramer’s Rule      70 349
Crank — Nicolson scheme      597
Cuthill — McKee algorithm      141—143 155 461
CYCLE      36 37
Degree      36 141 142 146—149 151 153—155
Descendant      139
Determinant      70 349 350
Diagonally dominant matrix      18 21 95—97 102 111 122 446 448 480 507 600
Diameter      37 141 142
Digraph      35 168 469 470
Direct methods      1 49 68 70 131 178
Dirichlet boundary conditions      44 50 52 54 55 177 204 405 415 436 439 443 448—450 452 453 467 488 493 542 597 599 640
Dissection      155—159 163 171 176 461 637
Distance      37 147 148 638
Dulmage — Mendelsohn decomposition      161 162
Eccentricity      37 38 141
Eigenvalues      9 10 12 13 16 21 27 31 33 50—55 67 68 178 188—190 201 210 212 213 217 218 220 222—224 228 231 232 242 244 247 248 266 268 269 271 274 275 277 278 281 284 286 287 292 293 298 300 304 310 311 321 322 335 336 339 348 349 351 384 394 397 398 402 403 405 407 408 410 415 428 430 432—442 444 447—450 452 460 478 487 491—493 509 511 520 525 526 528 544 547 548 551 554—556 602 606 608—610 612—614 616—619 621 624 630 631 636
Eigenvectors      9 10 51—54 56 178 189 201 221 222 275 284 286 292 293 428 432 437—440 452 478 545 548—551 554 555 557 608—610 613 630
Elimination tree      137 164 166 168 171—175
Energy norm      5 30 31 261
Envelope      140 145 149 152 176
Equimodular set      28
Euclidean norm      2—4 8 13 150 301 303 333 334 343 361 383 388
Fast Fourier Transform      179 180 206 531
Fill-in      132—134 137—139 141 152 153 156 165 167 171 176 200 305 417 423—426 465 467 468 470 472 478 480 508 509 648 649 651—653 655
Finite difference method      41 50 57 58 148 177 213 241 326 424 443 453 454 461 467 472 479 494 501 542 547 560 589 598 600 601 613 615 625 641
Finite element method      41 47 163 300 327 403 530 560 563 569 571 615 639 647
Floating point      1 2 49 59 60 62—66 68 70 81 82 85 134 256 258 303 315 329 334 345 351 354 372 380 383 386 388 391 475 571 572 634
Floating point arithmetic model      58
Forest      37
Forward error      120
Fourier analysis      56 57 68 179 191 202 399 409 415 428 430 432 448 453 493 557
Frobenius norm      5 6 450 451 463 466 469 504 652
Frontal method      163 176
Gauss quadrature rule      286 292 294
Gauss — Lobatto quadrature rule      294
Gauss — Radau quadrature rule      294
Gaussian elimination      62 66—68 70 111 112 117 121 122 128 129 131—135 164 169 170 173 175 191 192 199 200 215 315 340 461 471 530 535 586 601
Generalized diagonally dominant matrix      22 448
Generalized strictly diagonally dominant matrix      22 26—29 97
Gerschgorin disks      21 636
Gigaflops      64
Gram — Schmidt orthogonalization      7 11 281 338 357 508
Graph      35—37 134—137 141—143 148 150—152 156 157 159—161 163 164 168 468 470 471 475 534 561 652
Graph contraction      151
Growth factor      98 115 117 122
H-matrix      28 33 98 211 212 215 219 220 224 227 231 236 237 418—422 452 458 508
Hermitian matrix      12 392
Householder — John theorem      31 240
Induced matrix norm      4 5 16
Inner product algorithm      85 90
Irreducible      17 18 20 37 101 143
Irreducibly diagonally dominant      18 19 21 26 27 29 212 220
Iterative methods      1 2 14 17 29 33 38 39 44 50 56 68 209 213 248 250 262 295 309 310 315 339 397 399 541 543 545 576 586
Iterative refinement      121—123 169 170 543
L-matrix      24—28 212 480
LAPACK      67 68 128

Laplacian      43 56 58 562 613
Laplacian matrix      148 149 160
Level structure      37 38 141 146 637
LINPACK      65 67 68 92 128
LU factorization      76—78 81 91 98 99 102 103 114 125 323 340 367 368 371 417 602
M-matrix      24—29 31—33 97 98 149 212 213 220 225 237—239 249 420—422 448 469 494 508 580 598 602 648
Markowitz criterion      167
Matrix norm      3—5 14
Maximum norm      5 39 121 229 269
Maximum principle      24
MFLOPS      63
Minimum degree algorithm      142 146 152—155 163 167 171 176 651
Modified Gram — Schmidt      8 338 358 360 367 394
Monotone matrix      24
Multifrontal method      163 166 175
Multiprocessor computers      64
NETLIB      67 187
Neumann boundary conditions      45 632
Neumann series      17 511
Newton’s method      41
Norm      4 5 7 14—16 31 242 256 275 282 283 296 300 307 309 310 318 331 333 334 345—347 351 353 354 356 361 363 364 368 372 379 380 383 386 388 391 424 450 451 464 504 505 571
Normal equations      331 333—335 394
Normwise backward error      119
Normwise condition number      119
Normwise error analysis      118
Orthogonal matrix      8 12 188 244 266 358 364 531 608 613
Orthogonal polynomials      41 267 287 320 374 375 515
Orthogonality      7 8 244 254 279—281 308 310 312—315 317 318 320 323 329 341 349 354 358—360 362 375 378 379 392
Outer product      84 85 93 94 416
overlapping      586—588 592 594 596 597 599 600 642
Parallel algorithms      65 123 125 535
Parallel computers      63—65 67 170 171 176 183 228 260 504 532 534 538 577 585
Parallelism      64 67 125 170—172 175 186 199 215 223 327—329 394 399 401 461 507 533 535 537 576 586 595 596 603 605 635—637
Partial differential equations      41 47 186 203 214 229 326 443 541
Partial pivoting      79—81 117 121 122 167
Path      36 37 137—139 156 162 168 169
Periodic boundary conditions      45 46 50 53 54 178 200 399 405 409 428 430 447 450 482 486 488 557
Peripheral node      37 141
Permutation matrix      18 23 78—81 95 133 466 469
PetaFLOPS      64
Pipelined computer      63
Pivot      70 72 78—81 85 93 95 112 117 121 126 128 134 167 173 304 422
Pivoting      78 80 81 92 93 95 99 100 122 133 168 169 340 423 424
Poisson equation      42 50 177 184 399 604
Poisson model problem      44 47 50 111 145 159 178 187 213 229 300 337 400 403 408 427 443—447 452 453 458 467 476 478 482 511 542 571 588 592 602 610 613—616 618 625 638 651
Positive definite matrix      5 30—35 93 94 111 134 166 216 217 220 228 231 232 242 250 252 256 263—266 282 284 296 304 316 318 331 332 347 350 351 354 397 402 403 417 423 435 440 458—460 501 507 512 526 585
Powers of a matrix      14
Prime factor algorithm      187
Profile      140 141 145 148—150 417 475
Property A      23 218 221 228 400
Pseudo-peripheral node      141 142 146 637
QR factorization      307 313 319 338 339 342 344 358 394 506
Reachable node      137 139 162 168
Recursive bisection      159
Reducible matrix      18
Regular splitting      29 68 213 225 226 237 238 249 420 422
Roundoff error analysis      58 122 357 373
Roundoff errors      58 62 196 198 245 249 252 310—312 315 337 357 360
Saxpy algorithm      124
Scalability      65
Scalapack      67
Scalar product      2 3 7 10 39 85 124 252 254 256 316 326—328 332 366 392 592
Scalar product algorithm      125
Scaling      121 122 283 342 366 388 399 401 485 526 647
Schur complement      27 28 34 93 586 602 606 607 609 620 621 623 624 627—629 632 638 648
Section graph      37
Separator      37 156 159—162
Series of matrices      16 237
Sparsity      131 140 167 171 423 498 505 507 508 629
Spectral decomposition      12 178 188 195 313 320 610
Spectral norm      556
Spectral ordering      150 152 160
Spectral radius      13 14 210 213 217 221 229 233 242 469 548 556
Splitting      29 57 209 210 216 230 234 241 246 249 309 417
Storage scheme      49 50 132 140 182 326
Strictly diagonally dominant matrix      18 21—23 26—29 33 68 97 98 102 211 212 215 219 220 224 230 235 236 419 594 598 623
Subgraph      36 37
Symmetric positive definite matrix      30 94 131 176 215 216 231 232 240 241 243 251 261 266 332 333 336 397 398 400 402 407 417 455 456 458 459 476 510 544 583 602 605
Teraflops      64
Transitive closure      168
Transpose envelope      143
TREE      37 137 172 174 175
Tree rotation      172 173
Tridiagonal matrix      43 99 101 104 177 195 282 289 291—293 295 304 371 408 480 485 486 489 526 538 601 603
Twisted factorization      103 104 607 636
UL factorization      100 101 103
Unitary matrix      11 12 16
Vector computers      63—65 128 186 326 532—534
Vector norm      3 16 30
Wrap mapping      124 174

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