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| Bulirsch R., Stoer J. — Introduction to numerical analysis |
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| Предметный указатель |
 ,  norms 230
 -method of Aitken 162 312ff
 -rule (integration) 128
A-conjugate 321
A-stability 491 493
Abramowitz 156 166
Absolute error 12 295
Absolute norms 411
Absolutely continuous 88 94
Absolutely stable 490
Achieser 123
Adams — Bashforth methods 456ff
Adams — Moulton methods 456ff 476
ADI-methods 597 598ff 615 633
ADI-methods, convergence of 599ff
ADI-methods, optimal parameters of 603ff
Ahlberg 94
Aitken’s -method 162 312ff
Aitken’s interpolation algorithm 43 45 311
Algebraic multiplicity 332 336ff
Algorithm 9
Algorithm, graph of 19
Algorithm, numerically more trustworthy 17
Algorithm, numerically stable 18
Algorithm, well behaved 18
Alternating-direction implicit see “ADI”
Amplification of errors 14
Approximation error 1 2 57 127 128 129
Approximation method 90
Approximation through interpolation 51
Arithmetic operations 7
Arithmetic, complex 301
Arithmetic, fixed-point 3
Arithmetic, floating-point 5 11
Arithmetic, interval 27 28
Arithmetic, statistical error 32
Artificial variables 243
Ashenhurst 5 36
Associative law of arithmetic 8
Asymptotic expansion 126 140 144 148 445
Asymptotic expansion of central difference quotient 145
Asymptotic expansion of global discretization error 443ff 476ff
Asymptotic expansion of trapezoidal sum 125
Attenuation factors 91
Autonomous differential equation 491
Axelsson 609 613 636 643
B-splines 102 107ff 122
Babuska 522
Back-substitution 168
Back-substitution, round-off errors in 196ff
Backward analysis of errors 19 27
Backward deflation 294
Backward difference formula see “BDF”
Bader 491
Badly conditioned 305
Bairstow’s method 301ff
Banachiewicz’ method 175
Band matrix 176 547ff
Band width 176
Bank 495
Baptist 324 328
Barker 245 258 571 643
Bartels 221 258
Barth 371 425
Basic (feasible) solution 232
Basis of a linear program 232
Bauer 18 19 36 140 144 166 258 286 328 408 411 425
BDF-methods 493 494 498
Bendixson, theorem of 418
Benign 19
Bernoulli numbers 135
Bernoulli polynomials 137
Bessel functions 115
BFGS-method 318 322 324
Bidiagonal matrix 402 403 405
Bilinear form 541ff 554
Bisection method 157 299 371 502
Bit 3 4
Bit-cycling permutation 120
Bit-reversal permutation 81
Bjorck 207 258 646
Block Gauss — Seidel method 595
Block iterative methods 594
Block Jacobi methods 596
Block relaxation methods 596
Block single-step method 595
Block total-step method 595
Bloomfield 78 123
Blum 258
Bohmer 93 123
Boisvert 644
Boundary conditions, nonlinear, separated 499
Boundary-value problems 93 429 509 521
Boundary-value problems with free boundary 501 527
Boundary-value problems, linear 508
Boundary-value problems, model problem for 589 600ff 604ff 621ff
Boundary-value problems, singular 522 523
Bowdler 400 425
Boyd 549 567
Brandt 622 632 643
Brent 311 328
Briggs 622 644
Brigham 78 123
Broyden 318 328
Broyden, Fletcher, Goldfarb, Shanno see “BFGS”
Broyden’s rank-one method 284 318 520
Bulirsch 72 86 102 123 142 143 144 146 147 161 166 486 495 516 551 567
Bunch 167 258
Buneman 615
Buneman, algorithm of 571 614ff 621
Buneman, suggestion by 619
Bunse 426
Bunse — Gerstner 426
Butcher 439 567
Buzbee 615
Byrne 494 498 567
Cancellation 8 14
Canuto 549 567
Cauchy’s convergence criterion 264
Cayley — Hamilton Lemma 339
Central difference quotient 145
Chan 622 644
Characteristic polynomial 157 286ff 299 306 332ff 371ff 418 466
Chebyshev polynomials 156 165 611
Chebyshev system 153
Choleski decomposition 180ff 183 245ff 320 405ff 539 545 591 595 599 612
Choleski decomposition, incomplete 613 614
Ciarlet 57 123 258 548 559 560 567 646
CLIQUE 248
Clique representation 252ff
Coddington 433 567
Collatz 258 328 438 531 567
Collocation method 548
Collocation points 548
Column sum criterion 576
Complete pivot selection 169 195 196
Complex arithmetic 301
Complex conjugate roots 301
Composite of integration rule 129
Computers (digital, analog) 2 3
cond 187
Condition numbers 13 322
Condition of eigenvalue problem 351ff 377 414
Condition of linear equations 183ff
Condition of linear least squares 210ff
Condition of matrix 187
Conjugate-gradient method 571 606 607 610 633
Conjugate-gradient method for least squares 610
Conjugate-gradient method, preconditioned 613
Consistency condition 496
| Consistent initial values 496
Consistent matrix norm 185
Consistently ordered 582 583ff
Constrained minimization 261
Conte 646
Continuation methods 521ff
Continued fraction 65
Contraction property 267
Contractive mapping 267 316
Convergence, alternating 266
Convergence, cubic 395
Convergence, essential 384 385
Convergence, global 265
Convergence, linear 266 308
Convergence, local 265
Convergence, quadratic 266 270 290
Convergence, superlinear 323
Convex 269
Cooley 78 123
Cooley — Tukey method 78 119 120
Corrector methods 457 475 481 482
Courant, Weyl, theorem of 417
Covariance matrix 209
Cramer’s Rule 372
Crout’s method 174ff
Cubic convergence 395
Cubic splines 38 93 546
Cullum 366 426
Curry 110 123
Curvature 97
Dahlquist 475 493 567 646
Damping of errors 14 29 47
Daniel 222 225 258
Dantzig 230 233 243 258
Data fitting 205ff
Davenport 488 569
Davidon 318 323 328
Davidon, Fletcher, Powell see “DFP”
Davis 38 123 126 131 166
de Boor 93 97 102 114 123 646
de Doncker 159 166
Decimal number representation 3 4
Decomposition of maps 10
Decomposition, QR 198ff
Decomposition, triangular 172ff
Definite integral 125
Deflation 294 312
Deflation, backward 294
Deflation, forward 294 295
Degenerate linear program 232
Degree of a node 248
Degree type of rational interpolation problem 58
Dekker 307
Dennis 285 328
Derogatory matrix 338
Descent direction 317
Determinant 175
Deuflhard 328 491 495 498 522 525 566f
DFP-method 318 324
Diagonal matrix 192 337 359 425
Diagonalizable matrix 337ff 346ff
Diagonally dominant 576
Diagonally dominant, irreducibly 577
Diagram of degree types 62
Diekhoff 488 567
Difference equations 463ff
Difference equations, linear 464
Difference equations, stability condition for 465
Difference methods 535 570
Difference methods for ordinary differential equations 535 537 550 552
Difference methods for partial differential equations 588ff
Difference quotient, central 145 149
Difference quotient, one-sided 145
Differential equations, ordinary 93 136 428ff 535ff 550ff
Differential equations, partial 93 588ff
Differential error analysis 12
Differential operator 541
Differential operator, positive definite 542
Differential operator, symmetric 541 554
Differential-algebraic equations 494ff
DIGITS 1
Digits, leading 8
Digits, significant 4
Direct methods for linear equations 167ff 198ff
Dirichlet boundary-value problem 553 588
Discretization (discretizing) 1 125ff 144ff 614
Discretization error 1ff
Discretization error, global 439ff 443 444 476
Discretization error, local 437
Distributive law of arithmetic 8
Divided differences 43 44ff 48 54 63 107ff 311
Divided-difference scheme 45 49
Dividing off 294 297
Dixon 322 328
Domain decomposition methods 622
Dongarra 167 258
Dormand 454 567
Dorr 622 644
Double-step method 290ff 295
Drazin-inverse 497
Duff 245 253 258
Eberlein 362
Eigenproblem, generalized 323
Eigensolution 330
Eigenvalue problem 330
Eigenvalue problem for differential equations 500
Eigenvalue problem, algebraic 330
Eigenvalue problem, generalized 405
Eigenvalues 157 158 286 299 331 332ff 370
Eigenvalues, algebraic multiplicity of 332 336ff
Eigenvalues, exclusion theorems for 406
Eigenvalues, extremal properties for 417
Eigenvalues, geometric multiplicity of 333 336ff
Eigenvalues, ill-conditioned 377 414
Eigenvalues, multiplicity of 332 335ff
Eigenvalues, numerically acceptable 376ff
Eigenvalues, sensitivity of 411
Eigenvalues, well-conditioned 375
Eigenvector 157 158 331 332ff
Eigenvector, left 334 384 412ff
Eigenvector, numerically acceptable 376 378f
Eisenstat 253 259
Elementary divisors 337 340 376ff 414
Elementary inequalities 230
Elementary maps 10 17
Elementary operations 9 32
Elimination for sparse matrices 245ff
Elimination matrix 222 367
Elimination, Gauss —Jordan 177ff
Elimination, Gaussian 167ff
Embedded methods 453
End corrections 131
Enright 488
Equilibrated matrix 169 192ff
Equivalent rational expressions 59
Erdelyi 140 166
Erisman 245 253 258
Error amplification 14
Error analysis, backward 19 27
Error analysis, differential 12
Error bounds for Hermite interpolation 57
Error bounds for linear equations 183ff
Error bounds for linear least squares 209ff
Error bounds for spline interpolation 105ff
Error damping 14 29 47
Error distribution 30 32
Error propagation 11 18 20 31
Error, absolute 12
Error, approximation 1ff 57 127ff
Error, discretization 1ff 437 439ff 443 444
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