Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

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

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


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: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$L_1$, $L_{\infty}$ norms      230
$\Delta^2$-method of Aitken      162 312ff
$\dfrac38$-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 $\Delta^2$-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
1 2 3 4
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2018
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте