Bulirsch R., Stoer J. — Introduction to numerical analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Bulirsch R., Stoer J. — Introduction to numerical analysis

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Название: Introduction to numerical analysis

Авторы: Bulirsch R., Stoer J.

Аннотация:

This book contains a large amount of information not found in standard textbooks. Written for the advanced undergraduate/beginning graduate student, it combines the modern mathematical standards of numerical analysis with an understanding of the needs of the computer scientist working on practical applications. 35 illustrations.

Язык:

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second edition

Год издания: 1992

Количество страниц: 660

Добавлена в каталог: 19.02.2005

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Предметный указатель

Roundoff errors in Fourier synthesis      84ff
Roundoff errors in Gaussian elimination      191ff
Roundoff errors in linear least squares      213ff
Roundoff errors in one-step methods      445ff
Row sum (matrix) norm      186
Row sum criteria      576 577 614
Runge      438 569
Runge — Kutta method      438ff 443ff 450ff 479 488
Runge — Kutta — Fehlberg method      451 489 491ff
Rutishauser      72 102 123 140 144 166 259 331 360 362 380 427 646
Rutishauser’s semilogarithmic notation      4
Saad      365 427
Samelson      36
Sande      78 123
Sande — Tukey method      78 120
Sauer      36 123
Saunders      222 259 328
Sautter      197 259
Scaling      7 192 425
Scarborough      6 36
Schaback      646
Schoenberg      110 114 123 130 166
Schroder      622 644
Schultz      57 93 123f 253 259 548 567
Schultz’s method      326
schur      345
Schur norm      186
Schur normal form      345
Schur’s Theorem      347
Schwarz      257 259 362 427 526 560 569 646
Schwarz inequality      543 555
Schwetlick      426
Scott      366 426
Search direction      273
Seber      206 259
Secant method      308ff
Secrest      150 166
Sedgwick      488 568
Semi-implicit method      491
Semi-implicit midpoint rule      491
Semilogarithmic notation      4
Sensitivity to input perturbation of linear equations      187ff
Sensitivity to input perturbation of linear least squares      210ff
Sensitivity to input perturbation of polynomial roots      303ff
Seydel      488 567
Shampine      430 484 488 569
Shanks      439 569
Shanno      318
Sherman      253 259
Shift parameter      391
Shift techniques      392ff
Shooting methods, counter      564
Shooting methods, internal subdivision in multiple      520
Shooting methods, limiting case of multiple      531
Shooting methods, multiple      516ff 519ff 522 524ff 531ff 549 551
Shooting methods, simple      502ff 507 513ff 519ff 528 549 551
Shooting methods, starting trajectory      520ff 527
Sign-changes      297
Significant digits (bits)      4
Similarity transformation      334 351
Simple Kutta formula      561
Simplex method, general step      233
Simplex method, phase one      241ff
Simplex method, phase two      230ff
Simpson’s rule      125 127 128 132 134 140 439
Single-step method      573
Singleton      124
Singular value decomposition      349 400ff
Singular values      348ff 400ff
Slack variable      230
smith      331 356 357 368 380 400 427
Sobolov norm      555 559
SOR methods      580
SOR methods, optimal      635
Sparse matrix      183 245 571 591
Spectral methods      549
Spectral radius of matrix      407 574
Spedicato      322 329
Spline of degree k      97 102 107 110
Spline, cubic      38 93 546
Spline, exponential      122f
Spline, interpolation      38 93ff
Spline, natural      96
SSOR-matrix      613 635
Stability condition      465ff 469ff 472 474ff
Stable, numerically      18ff 85 368 619
Stationary point      275 277
Steepest descent method      606
Steffensen      127 134 166
Steffensen’s convergence acceleration      314ff
Stegun      156 166
Stein, Rosenberg, theorem of      579
Steinebach      495 498 569
Step length, geometrically increasing      147
Step length, sequences for extrapolation methods      140 161
Step length, size      131 430 435
Sterbenz      30 36
Stetter      430 439 569
Stewart      167 222 225 258f 406 426f
Stiefel      140 144 166 259 362 427 606 644 647
Stiff differential equations      488ff

Stoer      86 123 143 147 161 166 324 328f 411 425 486 551 567
Stopping criterion for extrapolation method      143 149
Storage technique      245
Stormer and Numerov, method of      539
Strang      560 569
Stroud      150 166
Sturm sequence      297ff 371
Submultiplicative norm      186
Subordinate norm      185
Subspace iteration      383
Successive overrelaxation      see “SOR”
Summation formula of Euler and MacLaurin      126 130 135ff 140
Superlinear convergence      323
Support, abscissas      37 129 146
Support, ordinates      37
Support, points      37
Swarztrauber      615 644
Symbolic factorization      247ff
Symmetric matrix      299
Symmetric rank-one method of Broyden      318
System of linear equations      153 167
Szabo      123
Szego      157 166
Tang      522 568
Teukolsky      646
Tewarson      245 259
Thiele’s continued fraction      67
Todd      647
Tornheim      327 329
Total-step method      573
Totally positive      114
Translation invariant      91
Trapezoidal, rule for integration      128ff
Trapezoidal, sum      89 125 129 131 136 139ff 142ff 149 161
Traub      286 310 328f
Triangle inequality      184
Triangular decomposition      246 595
Triangular decomposition by direct computation      174ff
Triangular decomposition by Gaussian elimination      167ff
Triangular decomposition by orthogonalization      198ff
Triangular decomposition, positive definite case      182
Triangular matrix      168ff 380ff
Tridiagonal matrix      156 286 306 331 353 364ff 380 395
Tridiagonalization      353
Trigonometric expression      72
Troesch      514 569
Trottenberg      622 632 644
Trustworthy, numerically      17 19
Tukey      78 123
Two-grid method      628ff
Uberhuber      159 166
Unconstrained minimization      261 272ff 316ff
Underflow of exponent      6 7
Underrelaxation      580
Unitary matrix      187 345ff 382ff
Upper Hessenberg matrix      226 352
van der Vorst      613 644
van Loan      167 259 331 389 426
Varga      57 123 548 567 571 579 581 583 596 597 600 602 603 638 641 642 644
Varga, Young, theorems of      586ff
Variable order method      483
Variance of random variable      209
Variance of roundoff distribution      32
Variational methods      540 545ff
Variational methods for ordinary differential equations      540 550 552
Variational methods for partial differential equations      553
Vector iteration      383 416 572
Vector iteration, simple      370 373 375 383
Vector iteration, Wielandt’s inverse      370 373 375 379ff 383 385
Vector norm      184ff
Vetterling      646
Vitasek      522 566
von Neumann      7 36
Wachspress      603 645
Wagschal      559 567
Walsh      94 123
Wanner      430 439 484 494 497 568
Watts      488 569
Weddle’s rule (integration)      128
Weight function      150
Weights in Gaussian quadrature      154 157
Weights in Newton — Cotes formulas      726
Weinstein, theorem of      415
Well behaved      18
Well-conditioned      13
Welsch      156 157 158 166
Werner      646
Weyl      see “Courant”
Whitney      114 123
Widlund      622 644
Wilkinson      19 36 167 175 195 207 213 214 239 259 294 295 297 305 306 307 329 331 356 357 362 368 371 380 386 395 398 400 406 425ff 497 569 574 609 633 645
Willoughby      245 259 366 426 488 494 569
Wittmeyer      572 645
Witzgall      62 123 411 425
Word length, double, triple      3
Young      571 582 597 602 603 642 645f
Young, Varga, theorems of      586ff
Zang      549 567
Zero of function      260ff 306ff
Zero suppression      295 312
Zlamal      558 559 569
Zugck      495 498 567

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