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