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Antia H.M. — Numerical Methods for Scientists and Engineers
Antia H.M. — Numerical Methods for Scientists and Engineers

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Название: Numerical Methods for Scientists and Engineers

Автор: Antia H.M.

Аннотация:

This book has evolved out of lecture courses delivered to Research Scholars at the Tata Institute of Fundamental Research during the period 1978-88. It attempts to provide a practical guide for numerical solutions to mathematical problems on digital computers. It is intended for both students and research workers in science and engineering. Readers are expected to have a reasonable background in mathematics as well as computer programming.
The enormous variety of problems that can be encountered in practice makes numerical computation an art to some extent, and as such the best way of learning it is to practice it. Attempting to learnnumerical methods by simply attending lectures or by just reading a book is like trying to learn how to play football by the same method. All students are therefore urged to try out the methods themselves on any problem that they may fancy, not necessarily the ones given in this book. In fact, the reader will probably not appreciate the contents unless he makes a serious attempt to usenumerical methods for solving problems on computers.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 977

Добавлена в каталог: 17.01.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$h\rightarrow0$ extrapolation      (see Extrapolation methods)
$L_{1}$ norm      395
$L_{1}$-approximation      395 459—461 873
$L_{2}$ norm      395 398
$L_{p}$ norm      394
$l_{\infty}$ norm      395
$\epsilon$-algorithm      185 203 207 208 212 233 430 585 783 862
$\epsilon$-table      185 223 233 784 862
$\hbar$      26 27 30 32 35 37—42 46—48 53 56 66 67 80—82 87 88 92 95 98 159 162 193 225 231 232 237 257 274 292 306 311 313 349 352 358 368 374 393 406 449 485 760 762 791 825 879 881 893
$\{x\}$      257
1.06      28 35 37 80 708
A-stable      556 557
Aarts, E. H. L.      387
Abramowitz, M.      51 161 189 199 236 437 709
Abscissa      118 172 188 194 195 200 245 246 602 923
Abscissa, finding nearest      126 769 771
Absolute convergence      13 723
Absolute error      26 222 315 544
Absolute stability      527 549 550 553 560 569
Accumulation of double length numbers      38 40 43 71 80 82 105 504 762
Acton, F. S.      324 326 393 450
Adams      562 898 899 903
Adams method      536 538 558 562 654 898 903
Adams method, roundoff error      591
Adams method, stability      530 560 745
Adams — Bashforth formula      535
Adams — Moulton formula      527 536
Adams — Moulton formula, stability      530
Adaptive integration      207 209 211 216 219 223—226 227 231 538 592 611 793
Adaptive integration, global      224 226
Adaptive integration, local      223
ADI      683 931 943
ADM      935
ADPINT      208 209 210 211 216 223 224 225 226 229 230 231 232 618 793 927
Advanced computer arithmetic      33
AEPS      754
Ahlberg, J. H.      134
Ait ken’s method      185 203 278 335 481 515
Alefeld, G.      33
Algebraic manipulation program      156 688
Aliasing      415 424 427
Aliasing, Chebyshev polynomials      439
Alternating direction implicit iterative (ADI) method      681—683 943
Alternating direction implicit iterative (ADI), parallel processing      693
Alternating direction implicit iterative (ADI), rate of convergence      683
Alternating direction method      656—658 681 935
Alternating direction method, boundary conditions      657 697
Alternating direction method, parallel processing      691
Alternating direction method, stability      657
Alternating direction method, three space variables      657
Alternating direction method, truncation error      697 750
Alternating variables method      363
Always convergent methods      272 291 293 294 295 305 308 314 347 357
Amplification factor      642 644 656 657 660 665 669 697 698 750 751
Amplification matrix      662 699 750 751
Analytic function, interpolation      148
Analytic function, zeros      302—305 820
Approximation      117 392—473 734—741 855-875
Approximation of data      393 397—414 454—461 855
Approximation of mathematical functions      393 431—454 863 865 867
Approximation, $L_{1}$      395 459—461 873
Approximation, Chebyshev      395 437
Approximation, chi-square      396 398 399
Approximation, choice of model      396
Approximation, degenerate      449 453
Approximation, differentiation      405 409 414 458 460 463 857
Approximation, error in      397 411 432 441 460
Approximation, Fourier      397 417
Approximation, ill-conditioning      399 403 449 459
Approximation, interpolation      117 394 609
Approximation, least squares      395 397—414 855
Approximation, linear      396 397—409 455 459 855 873
Approximation, minimax      395 446—458 471—473 738-740 867—872
Approximation, Monte Carlo simulation      411 460
Approximation, multivariate      414 466 473
Approximation, nonlinear      397 409—414 456
Approximation, Pade      431—437 863
Approximation, rational function      431—454 456 457 863 865—872
Approximation, roundoff error      401 406 407 408 412 450 451 454 468 469
Approximation, smoothing      394 404 413 417 458 460
arc sin      (see $sin^{-1}x$)
Arc tan      (see $tan^{-1}x$)
Archimedes      17 170
Array in Fortran      9 427 860
Artificial damping      663 665
Artificial pole      449 453
Artificial variables      383 391 851 852 853 854
Artificial viscosity      663
Associative law      28 29 34 39 54
Asymptotic error constant      285 336 353
Asymptotic series      13 16 17 121 181 234 471
Automated allocation of mesh points      586 588
Automatic integration      218—233 780—805
Automatic integration, adaptive      219 223—226 793
Automatic integration, iterative      219 780 782—791 795—805
Automatic integration, limitations      219 226
Automatic integration, multiple integrals      243 795—805
Autonomous form      522
Average      396
Avoided crossing      745
Back-substitution      65 69 75 86 107 135 485 581 757 760 771
Back-substitution, roundoff error      80
Back-transformation      493 500 509 878 880 891
Backward deflation      341
Backward difference      128 262 571
Backward differentiation formula      161 558
Backward error analysis      34 38 39 43 45 79 81 343 512 609
Backward Euler’s method      536 557
Backward interpolation formula      128 151 527 535 539
Baker, C. T. H.      598 622 628
BALANC      503 510 888 891
Balanced-decimal      52 704
Balanced-ternary      21 704
Balancing a matrix      502 503 510 888
Balancing a matrix, isolated eigenvalue      503
balbak      503 891
Band matrix      62 96 97 107 109 494 579 653 673
Band matrix, Gaussian elimination      65 97 107 109
Bandwidth      62 96 97 672 673 690
Bandwidth limited      415
Barrodale, I.      456 459
Base      18 19 20 21 23 26 47 52 502 755 888
Basic feasible vector      380 383 385 851 852 853
Basic feasible vector, degenerate      380 381 391 457
Basic feasible vector, finding      383
Basis functions      398 455 459 608 610 685 926
Basis functions on parallelograms      688 702 752
Basis functions on triangles      687 702 752
Basis functions, biquadratic      702 752
Basis functions, cubic      702 752
Basis functions, finite elements      685 686
Basis functions, linear      687
BCs      910 911 913 914 916 922
BCSD      913 914 916
Beale, E. M. L.      391
Bernoulli numbers      181 233 234
Bernstein, S. N.      118
Bessel function      58 59 472 594 740 747
Bessel function, zero      337 594 747
BFGS      367 369 370 412 842 844 868
BFGS formula      365 368 389 842
BICUBC      777
BICUBE      777
Bicubic spline      146—148 155 777
Bidiagonal matrix      89 91 765
Biharmonic equation      701
Bilinear approximation      688
Bilinear interpolation      144
Binary complex system      21 704
Binary number system      19 20 22 24 419
Binary search      126 769 771 776
Binary tree      36 102
Biorthogonality      476 505
BISECT      274 351 808
Bisection      273—276 281 292 295 347 808
Bisection on parallel processors      334
Bisection, pitfalls      273
Bisection, roundoff error      274
Bisection, searching an ordered table      126 769 771 772 776
Bisection, Sturm sequence      494—497 883 884
Bit      22 24
Bit reversal      420 858 860
Block tridiagonal matrix      672
Bluestein’s FFT algorithm      422
Blunder      3 17 357 368 394 396
Boole’s rule      175
Boor, C. de      221 226
Bose — Einstein statistics      267
boundary conditions      521 564 571 572 600 914
Boundary conditions, alternating direction method      657 697
Boundary conditions, Cauchy      635 637 659
Boundary conditions, cubic spline      135 152
Boundary conditions, Dirichlet      635 638 639 640 674 684 689
Boundary conditions, finite difference methods      572 640 650 656 657 659 665 671 674 676 684
Boundary conditions, finite element methods      689
Boundary conditions, irregular boundary      674—676
Boundary conditions, Lax — Wehdroff method      665 939
Boundary conditions, Neumann      635 638 639 640 671 676 685
Boundary conditions, parallel processing      692
Boundary conditions, partial differential equations      635 638 639 640 650 656 657 659 665 671 674 676 684 689 931 932 936 939 943
Boundary conditions, periodic      684 701
Boundary conditions, separable      564 574 910 913 922
Boundary value problem      521 564—584 602 910
Boundary value problem, choice of method      570 578
Boundary value problem, conversion to integral equation      600
Boundary value problem, deferred correction      572 573 574 595
Boundary value problem, existence and uniqueness of solution      565
Boundary value problem, finite difference methods      565 571—578 910
Boundary value problem, initial value method      565—570 595
Boundary value problem, linear      566 568 572 576
Boundary value problem, nonlinear      565 569 574 577
Boundary value problem, partial differential equations      635 670—685 941 944
Boundary value problem, shooting method      565—570 595
Bracketing complex roots      296—298 814
Bracketing minimum      347 350 351 366 835
Bracketing Teal roots      273 278 280 283 291 295 307 324 807
BRACKM      351 388 835
Brent      292 812
Brent, R. P.      291 292 352 354 372 373 374 375 812 838
BRENTM      354 838 867 868 870
Brent’s method      290 291—295 566 812
Brent’s method for minimization      354—356 449 450 453 838
Brent’s method multiple roots      293
Brent’s method pitfalls      294
Brent’s method roundoff error      295
Brent’s method, convergence      291
Brigham, E.      0 424
Brownlee, K. A.      393
Broyden, C. G.      365
Broyden’s method      332—334 411 558 559 566 574 833 905
BROYDN      830 831 833
Bug      3 11 12 15
Bulirsch, R.      140 554 568 684
Buneman, O.      684
Burgers’ equation      696
Butcher, J. C.      593
Carry      21 23
Cartesian grid      144 296
Cartesian product      241
Cascade sum      36 40 193 754
Cascade sum, parallel processing      102 103 106
Cascade sum, roundoff error      37
Cauchy condition      635 637 638 639 659
Cauchy principal value      201 207 214 266
Cauchy’s Theorem      302
Causality      638
Cautious iteration      221
Cayley — Hamilton theorem      518
Central difference      463 650 671
Central difference formula      161 571 659 671
Central limit theorem      250
Centroid      246
Centrosymmetric      630
Chaining      100
Change of variable      203 213 243
Characteristic equation      475 525 528 529 558 559 582
Characteristic polynomial      318 475 476 478 590
Characteristic polynomial, Krylov’s method      518
Characteristics      636 638 639 659 660
Charles XII      20
Chasing      91
CHEBAP      865
CHEBCF      437 438 864
Chebyshev approximation      395 437
Chebyshev economization      441 442 469 738
Chebyshev expansion      437—446 447 864 866
Chebyshev expansion, calculating the coefficients      445 469
Chebyshev expansion, Lanczos $\tau$-method      470
Chebyshev expansion, rational function approximation      440 444 865
Chebyshev integration      194 263
Chebyshev interpolation      127 129 736
Chebyshev polynomials      59 127 196 197 198 340 388 437—440 449 597 610 864
Chebyshev polynomials, differentiation      440
Chebyshev polynomials, extrema      127 438
Chebyshev polynomials, integration      469
Chebyshev polynomials, orthogonality relation      439
Chebyshev polynomials, recurrence relation      437 438 469
Chebyshev polynomials, shifted      469
Chebyshev polynomials, zeros      127 196 438
Chebyshev SOR method      692
Chebyshev theorem      127 446
Cheney, E. W.      447
Chi-square      396 398 399
Cholesky decomposition      73 112 360 478 519
Chvatal, V.      391
clarity      10
Clenshaw, C. W.      220 471
Clenshaw’s recurrence      407 438 465 857
Cody, W. J.      449 454 472
Collocation      132
Collocation method      609 610 611 617 618 688 926
Collocation method, eigenvalue problem      613
Collocation method, Fredholm equations      609 610 611 617 618 926
Collocation method, partial differential equations      689
Combinatorial optimization      346 387
Commutative law      30
Complete pivoting      66 80 98 711
Complex arithmetic      29
Complex roots      296—305 308—312 814 829
Complex roots of analytic functions      302—305 820
Complex roots of polynomials      308—312 825—829
Complex roots, locating      296—298 814
Complex roots, Muller’s method      298—302 816 818
Complex roots, quadrature based method      302—305 820
complexity      65 122
Composite formulas      175 190 199 248 606
Composite formulas, convergence      177
Computational efficiency      287 299 310 336 339 353 357 729
Computational efficiency on parallel computers      334
Computer programming      (see Program/programming)
Condition number      44 46 154 512 609 709 717
Condition number of matrix      78 79 81 85 87 94 609 618 710 712
Condition number, nonlinear equations      319
Confidence level      251 254 803
Conjugate directions      371 376
Conjugate gradient method      99 365 370 376
Conjugate gradient method, Fletcher — Reeves method      376
Conjugate gradient method, sparse matrix      377
Conjugate transpose      63
Connection conditions      588
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