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| Авторизация |
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| Поиск по указателям |
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| Bulirsch R., Stoer J. — Introduction to numerical analysis |
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| Предметный указатель |
Error, inherent 18
Error, input 1
Error, integration 131
Error, interpolation 57
Error, relative 12
Error, roundoff 1ff
Error, truncation 1ff
Essential convergence 384 385
Euclidean (vector) norm 184 278 322 352
Euclidean algorithm 298
Euler — Maclaurin summation formula 126 130 135ff 140
Euler’s method 435ff 442 445 477 489ff
Euler’s method, implicit 489ff
Euler’s method, modified 438ft
Euler’s method, region of absolute stability for 490
Evaluation of characteristic polynomials 288
Evaluation of polynomials 44
Evaluation of trigonometric expressions 84ff
Exact line search 276 320ff
Exclusion theorems 406
EXPONENT 4
Exponent over(under) flow 6 7
Exponential interpolation 38
Exponential spline 122f
Extended integration rules 129
Extrapolation 51
Extrapolation methods 38 71 126 136
Extrapolation methods for differential equations 445
Extrapolation methods for differentiation 145
Extrapolation methods for initial value problems 484 486 489 504 491 498 551
Extrapolation methods for integration 139ff 159
Factorization, numerical 247ff
Factorization, symbolic 247ff
Fast Fourier transforms 38 78ff 549
Feasible point 230
Fehlberg 439
Fellen 488
Fibonacci sequence 561
Fike 408
Finite element method 553 557 560 570
fix 560 569
Fixed point 264
Fixed-point representation 3 4
Flannery 646
Fletcher 318 328
Floating-point arithmetic 4ff 15ff 445ff
Floating-point operations 7ff
Floating-point representation 4ff
Floating-point representation, normalized 4ff
Floating-point representation, unnormalized 5
Forsythe 259 574 644 646
Forward deflation 294ff
Fourier analysis 37
Fourier coefficients 88
Fourier series 88
Fourier synthesis 84
Fourier transform 37 78
Fractional iteration 375
Francis 331 380 382 398 426
Francis, observation of 403ff
Frazer, Duncan, Collar, method of 344
Free variable 231
Frobenius matrices 169 340 342ff 362
Frobenius normal form 340 342 362 418 466
Froberg 587 646
Fully nondegenerate rational interpolation problem 62
Gantmacher 497 567
Garbow 331 426
Gass 230 243 259
Gauss — Jordan method 177ff
Gauss — Newton method 218ff
Gauss — Seidel method 573 578ff 581 587 591ff 594 633 635
Gaussian elimination 102 167ff 191ff 368 380 519
Gaussian integration (quadrature) 126 129 150 159 161
Gauss’ arithmetic-geometric mean algorithm 603
Gautschi 91 123 156 166
Gear 430 484 494 498 567f
Generalized, eigenproblem 323
Generalized, inverse 2l8ff
Generalized, Lagrange polynomials 53
Generalized, spline functions 97
Gentleman 78 123
Geometric multiplicity 333 336ff
Geometrically increasing step length 147
George 245 251 253 259 622 644
Gershgorin’s theorem 408ff 488 537
Gill 222 259 328
Ginsburg 633
givens 426
Givens method of 358ff
Givens reflection 224 402ff
Givens rotation 224 359 390 397
Global discretization error 439ff 443 444 476
Globally convergent 265
Glowinski 622 644
Goertzel 84 123
Goldfarb 318
Goldstein 7 36
Golub 156 157 158 166 167 222 259 286 328 331 389 400 405 426 622 644
Golub and Reinsch, method of 331 400 401 404
Gordon 430 484 569
Gottlieb 549 568
Gradient 273
Gragg 222 225 258 443 479 480 568
Gragg’s function 484
Gram — Schmidt orthogonalization 151 203ff
Gram — Schmidt orthogonalization with reorthogonalization 205
Graph of algorithm 19
Graph of matrix 576
Graph of matrix, (weakly) 2-cyclic 585 592
Graph of matrix, connected 576 592
Graph of symmetric matrix 247
Great circle distance 35
Green’s formula 554
Gregory 646
Greville 93 97 123
Grid function 623
Griepentrog 497 568
Grigorieff 430 439 488 494 568
Grimm 516 525 552 568
grobner 125 166
Gropp 622 644
Grossman 206 259
Guest 206 259
Gursky 253 259
Haar condition 153
Hackbusch 622 632 636 644
Hadley 230 243 259
Hairer 430 439 443 479 484 494 495 497 498 567f
Hall 106 123 329
Hamilton see “Cayley — Hamilton”
Hammerlin 646
Handbook of Mathematical Functions 156
Hanson 207 259
Harmless round-off errors 18
Hausdorff 416
Heinhold 36
Helmholtz equation 622
Henrici 36 131 166 286 297 328 430 431 568 646
Hermite, function space 56 548
Hermite, interpolation 49 52ff 111 128 134
Hermite, polynomials 156 162
Hermitian matrix 161 331 345ff 417
Herriot 102 123
Hessenberg matrix 195 226 331 352 356 368ff 372 380 389ff 398ff
Hessenberg matrix, irreducible 390ff
Hessian matrix 285
Hestenes 526 568 606 644
Heun 438 568
Heun, method of 438ff
| Hildebrand 646
Himmelblau 261 328
Hindmarsh 494 498 567
Hirsch 406 418
Hockney 615 644
Hoffmann 646
Hofreiter 125 166
Holladay’s identity 94
Homogeneity axiom 184
Homotopy methods 521ff 524
Horneber 495 568
Horner scheme 44 84 287 303
Householder 199 259 290 328 411 415 644 646
Householder transformation for arbitrary matrix 356
Householder transformation for symmetric matrix 355
Householder, matrix 201
Householder, method of 353 358ff 362 370 401
Householder, orthogonalization 199ff
Householder, reduction 357 369
Hull 488 494 567f
Hussaini 549 567
Hyman 372
Hyman, method of 372
Ill-conditioned 13
Implicit differential equations 191ff
Implicit methods for differential equations 456 489
Implicit shift techniques 398ff
Improper integrals 162
Inaccessible points 61
Inclusion theorems 406 414
Incomplete Cholesky factorization 613 614
Indefinite integral 125
Index of nilpotency 496
Index-1 assumption 497
Inequalities, elementary 230
Inequalities, linear 230
Inexact line-search 276
Initial (starting) values, rules for the selection of 288 294 295
Initial-value problem 428 431 434
Integral, definite 125
Integral, improper 162
Integral, indefinite 125
Integration by parts 88 89 136 138
Integration rules of Gauss 126 129 750 159
Integration rules of Milne 128
Integration rules of Newton — Cotes 126 128ff 134 141 144 159 455 460
Integration rules of Simpson 125 128 130 132 134 141
Integration rules of Weddle 128
Integration rules,  128
Integration rules, composite (extended) 129
Integration rules, general form of 131
Integration rules, trapezoidal 128 132
Integration, error 131
Interpolation by B-splines 112ff
Interpolation error 49 57
Interpolation formula of Lagrange 39 52 126 146
Interpolation formula of Newton 62ff 310 311
Interpolation on product spaces 116
Interpolation operator 627
Interpolation, exponential 38
Interpolation, Hermite 49 52ff 128 134
Interpolation, inverse 311
Interpolation, linear 37
Interpolation, polynomial 37ff
Interpolation, rational 38 58ff
Interpolation, spline 38
Interpolation, trigonometric 72ff
Interval arithmetic 27 28
Inverse differences 63ff
Inverse interpolation 311
Inverse iteration of Wielandt 370 373 375 379 380 400
Inverse of matrix 167 177ff
Irreducible matrix 576ff 581 585
Irreducibly diagonally dominant 577
Isaacson 568 646
Iteration function 261 286
Iterative methods 570 588
Iterative methods for linear equations 570
Iterative methods for minimization 261 272ff 316ff
Iterative methods for roots of polynomials 286ff
Iterative methods for zeros of functions 260ff 306ff
Iterative methods, construction of 261ff 571
Iterative methods, convergence of 264ff 316ff 574ff
Iterative refinement 571 573
Jacobi matrix 353
Jacobi method 358ff 400 573 575 577 579 581 587 591 593ff 624 633 635
Jacobi method, damped 625 628 631
Jacobian elliptic function 505 515ff
Jacobian matrix 13 15ff 263 269
Jenkins 286 328
Jordan block 337
Jordan normal form 335 336ff 407 496
Kahan, theorem of 581
Kahaner 159 166
Kaniel 365 365 426
Kantorovich see “Newton — Kantorovich”
Kaps 491 492 568
Karlin 114 123
Kaufman 222 225 258
Keller 430 509 516 564 568 646
Keyes 622 644
Kielbasinski 426
Knots of splines 93
Knuth 36
Krogh 484 568
Kronrod 159 166
Krylov sequence 341 344
Krylov space 362ff 610
Kublanovskaya 380 426
Kulisch 30 36
Kuntzmann 123
Kutta 438 568
Lagrange polynomials 39 115
Lagrange polynomials, generalized 53
Lagrange’s interpolation formula 39 52 126 146 455
Lagrange’s interpolation formula, generalized 128
Laguerre polynomials 156 162
Lambert 494 568
Lanczos 362 426
Lanczos algorithm 362ff 365
Laplace operator 560
Lauchli 214
Lawson 207 259
Leading digits 8
Least-squares problem 207ff 210ff 610
Least-squares problem, nonlinear 217ff
Left eigenvector 334 384 412ff
Legendre polynomials 155
Leibniz formula 110
Levinson 433 567
Lindberg 494 567
Line search 317 319ff 324ff
Line search, exact 276 320
Line search, inexact 276
Linear approximation method 90
Linear convergence 265 308
Linear equations, direct methods for 167ff 198ff
Linear equations, elimination methods for 167ff 198ff 245ff
Linear equations, iterative methods for 570
Linear equations, positive definite systems of 180ff 245ff
Linear implicit systems 495
Linear multistep methods 471ff 476
Linear programming 230ff
Linearization 263
Linked list 246
Lions 258 560 567 646
Lipschitz condition 88 323 430ff 442
Lipschitz continuous 323 468
Liu 245 251 253 259 571
Local discretization error 437 459
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