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| Авторизация |
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| Bulirsch R., Stoer J. — Introduction to numerical analysis |
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| Предметный указатель |
Local minimum 265 320
Locally convergent 265
Lory 488 567
LP(I, p) 230
LR-method 331 370 380ff
Lub 186
Lubich 443 479 495 568
Luenberger 318 328
M-matrices 613 6/4
Machine numbers 4ff 8
Machine precision 6 8 86 462
Maehly 62 123 294 328
Maehly’s modification of Newton’s method 295 371
Malcolm 646
Mantissa 4 7
Marden 290 328
Martin 356 357 368 371 400 406 425f
Marz 497 568
Matrix norm 184ff
Matrix pencil 497
Matrix upper Hessenberg 195 226 352
Matrix with property A 582 583ff 592
Matrix, band 176 547 548
Matrix, bidiagonal 402ff 405
Matrix, block tridiagonal 584 596
Matrix, consistently ordered 582 583ff
Matrix, derogatory 338
Matrix, diagonal 192 337 359 425
Matrix, diagonalizable 337ff 346
Matrix, diagonally dominant 576 577
Matrix, Frobenius 169 340 342ff 418 466
Matrix, Givens 224
Matrix, hermitian 181 331 345ff 417
Matrix, Hessenberg 195 226 331 352 356 368ff 372 380 389 390ff 398ff
Matrix, Householder 199 353 357 366 382 401ff 426
Matrix, irreducible 370 372 576ff 581 585
Matrix, Jacobi 353
Matrix, nonderogatory 338ff
Matrix, normal 331 345 347 416
Matrix, normalizable 337 411
Matrix, orthogonal 187
Matrix, permutation 120 169 366 583
Matrix, positive (semi) definite 180ff 245ff 321 347 599 610
Matrix, sparse 571 591
Matrix, symmetric 119 176 181 299
Matrix, triangular 168ff 380ff
Matrix, tridiagonal 195 306 331 353 380 395
Matrix, unitary 187 345ff 383 387 391 392 398 399
Maximum norm 184
McCormick 632 644
Meijerink 613 644
Merten 495 567
Method of false positions see “Regula falsi”
Metropolis 5 36
Meurant 622 644
Meyer 106 123
Midpoint rule 439 458 460 476 484
Midpoint rule, modified 484
Milne 62 123
Milne — Thompson 66 123
Milne, corrector method of 458 476
Milne, integration rule of 128 142
Minimal degree algorithm 248 250
Minimal polynomial 338ff
Minimization, constrained, linear 230ff
Minimization, constrained, nonlinear 261
Minimization, unconstrained, general 261 272ff 316ff
Minimum point 206 217 261 316
Minimum point, local 317
Minimum-norm property 94
Model problem 589 600ff 604ff 614 621ff
Modification of matrix decomposition 221ff
Modified Newton method 272ff
Moler 167 258f 406 426 574 644 646
Moments of cubic splines 97
Moore 30 36
more 328
Muller’s method 310ff
Multigrid methods 622ff
Multigrid V-cycle 631
Multiple root 310
Multistep methods 455 489 493
Multistep methods, consistency of 460 472ff
Multistep methods, convergence of 461 467 472ff
Multistep methods, linear 471ff
Multistep methods, of order p 460 474
Multistep methods, step control for 481
Multistep methods, weakly unstable 480
Murray 222 259 286 328
Murty 243 259
Na 522 568
National Bureau of Standards 156
Natural spline 96
Neighboring basis 233
Nersett 430 439 484 568
Neumann see “von Neumann”
Neville’s interpolation algorithm 40ff 43 45 67 140
Newton direction 317
Newton form of polynomial 44 47 55
Newton — Cotes integration formulas 126 128ff 134 141ff 144 159 455 460
Newton — Kantorovich, Theorem of 272
Newton — Raphson method 262
Newton’s interpolation formula 43 62 310ff 481
Newton’s interpolation formula, error term for 50
Newton’s method for minimization 272ff
Newton’s method for roots of polynomials 286ff
Newton’s method for systems of equations 260 518 520
Newton’s method for zeros of functions 262ff 269ff
Newton’s method, approximate 507
Newton’s method, general 505 531
Newton’s method, Maehly’s version of 295 371
Newton’s method, modified 272ff 507 513 518 520 521 530
Ng 253 259
Nickel 286 328
Nielson 615 621 644
Nilpotent 496
Nilson 94 123
Nonbasic variable 232
Nondegenerate linear program 232
Nonderogatory matrix 338ff
Norm 13 184ff
Norm, absolute 411
Norm, consistent 185
Norm, Euclidean 184
Norm, maximum 184
Norm, Sobolev 555 559
Norm, submultiplicative 185
Norm, subordinate 186
Normal equations 206 207 610
Normal matrix 331 345 347 416
Normalizable matrix 337 411
Normalized floating-point representation 4
Numerical factorization 247ff
Numerically stable 18ff 85 368 619
Numerically trustworthy 17 19
Numerov see “Stormer”
Nystrom’s predictor method 457
Oberle 488 516 525 552 567f
Objective function 230
Oden 560 568
Oettli 189 259
Olver 140 166
One-step methods 434 436 491
One-step methods, consistency of 437
One-step methods, convergence of 439 440
One-step methods, embedded methods 453 454
One-step methods, of order p 437
One-step methods, step control for 448 450ff 453
Operand set 10
Opposite terms 79
| Optimal block relaxation methods 596
Optimal parameters of ADI methods 603ff
Optimal solution of linear program 231
Ordinary differential equations 428ff
Ordinary differential equations of first order 429
Ordinary differential equations of mth order 429
Ordinary differential equations, boundary-value problem for 429
Ordinary differential equations, initial-value problem for 428
Ordinary differential equations, systems of 428
Oren 318 322 328
Oren — Luenberger class 318 323ff
Orszag 549 568
Ortega 272 329
Orthogonal basis 75
Orthogonal matrix 199
Orthogonal polynomials 150 151ff 363
Orthogonal projector 219 221
Orthogonalization to solve least squares 209ff
Orthogonalization, Gram — Schmidt 203ff
Orthogonalization, Householder 198ff
Osborne 516 568
Ostrowski 311 329
Ostrowski, Reich, theorem of 581
Overflow of exponent 6f
Overrelaxation 580 581
Overshooting 290 294
O’Leary 622 644
Paige 365 366 426
Parlett 331 362 366 389 426
Partial pivot selection 169 171 178 195ff 379 381
Partially interpolating polynomials 41
Partition of unity 109
Peaceman and Rachford ADI method of 597ff
Peaceman and Rachford, formula of 641ff
Peano kernel 132 134
Peano’s error representation 125 131
Periaux 622 644
Permutation matrix 120 169
Perturbation of polynomial coefficients 303
Pesch 488 567
Peters 294 295 297 306 307 329 380 400 406 427
Petzold 495 498 568
Phase matrix 382
Phase polynomial 73ff
Phase, one of simplex method 241ff
Phase, two of simplex method 230ff
Piecewise polynomial function 107ff
Piessens 159 166
Pinkus 114 123
Pivot clique 250
Pivot element 169
Pivot element, complete selection of 169 195ff
Pivot element, partial selection of 169 171 178 195ff
Pivot element, selection 169 191ff
Pivot vertex 249
Poisson equation 614 622 636
Poisson equation, discretized 614
Polygon method 435
Polynomial characteristic 157 286ff 299 306 332ff 371ff 418 466
Polynomial interpolation 37
Polynomial, minimal 338ff
Polynomials, Bernoulli 137
Polynomials, Chebyshev 156 611
Polynomials, Hermite 156
Polynomials, Lagrange 39
Polynomials, Laguerre 156
Polynomials, Legendre 155 164
Poole 389 426
Positive (semi) definite 180ff 245ff 321 347 599 610
Powell 318 323 328f
Prager 189 259 522 566
Preconditioned conjugate gradient method 612
Preconditioner 612 635
Preconditioning technique 612
Predictor methods 457ff 475 481ff
Press 646
Prince 454 567
Principal vector 337
Projection operator 626
Proskurowski 622 644
Pseudoinverse of matrix 218ff 350ff
QR decomposition 198ff 382ff
QR method 157 158 331 370 372 380ff 403 405
QR method with shifts 392 395 403
QR method, convergence of 383 395
QR method, implicit shift techniques 398ff
QR method, practical realization of 389ff
Quadratic convergence 266 270 290
Quadratic function 320
Quadrature (Gaussian, numerical) 125 150
Quarteroni 549 567
Quasi-Newton equations 317 319
Quasi-Newton methods 317ff
Quasilinear-implicit systems 495
Quasilinearization 531
QZ method 406
r-step method 458
r-step method, linear 458
Rabinowitz 126 131 166 646
Rachford see “Peaceman”
Rademacher 30 36
Ralston 646
Random variable 30 209
Rank-one modification 225 318
Rank-two modification 286 316ff
Rational expressions 59
Rational expressions, equivalence of 59
Rational expressions, relatively prime 59
Rational functions 58
Rational interpolation 38 58
Rational normal form 340 342
Rayleigh quotient 416
Rayleigh — Ritz method 557
Rayleigh — Ritz — Galerkin method 93 540
Reciprocal differences 66
Reddy 560 568
Reduced costs 235
Reduction methods 615
Region of absolute stability 490
Regula Falsi 307ff
Regular matrix pencil 497
Reich see “Ostrowski”
Reid 245 253 258f 609 644
Reinitialization 285
Reinsch 86 91 102 123f 167 207 239 259 331 356 400 405 426f 574 609 633 645
Relative error 12
Relatively prime 59
Relaxation methods 579 580 633
Relaxation methods, convergence of 581
Relaxation methods, optimal 593ff
Relaxation parameters 580
Relaxation parameters, optimal 587 593 596
Rentrop 488 491 492 495 498 567ff
Reorthogonalization 205 366
Restricted variables 231
Reutersberg 622 636 644
Rheinboldt 261 264 272 329
Rice 644
Right eigenvector 332 384 412 413
Roche 495 498 568f
Romberg 140 142 166
Romberg’s integration method 126 140ff 146
Roots of polynomials 152 157 260 286
Roots of polynomials, complex (conjugate) 301 310
Roots of polynomials, multiple 310
Roots of polynomials, simple 292
rose 245 248 250 259
Rosenberg see “Stein”
Roundoff error distribution 30ff
Roundoff errors in back-substitution 196ff
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