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Hamming R.W. — Numerical methods for scientists and engineers
Hamming R.W. — Numerical methods for scientists and engineers

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Название: Numerical methods for scientists and engineers

Автор: Hamming R.W.

Аннотация:

Numerical methods use numbers to simulate mathematical processes, which in turn usually simulate real-world situations. This implies that there is a purpose behind the computing. To cite the motto of the book, The Purpose of Computing Is Insight, Not Numbers. This motto is often thought to mean that the numbers from a computing machine should be read and used, but there is much more to the motto. The choice of the particular formula, or algorithm, influences not only the computing but also how we are to understand the results when they are obtained. The way the computing progresses, the number of iterations it requires, or the spacing used by a formula, often sheds light on the problem. Finally, the same computation can be viewed as coming from different models, and these different views often shed further light on the problem. Thus computing is, or at least should be, intimately bound up with both the source of the problem and the use that is going to be made of the answers—it is not a step to be taken in isolation from reality.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1987

Количество страниц: 721

Добавлена в каталог: 03.04.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$z$ transform      644
$\Gamma$ function, table of      175
Absolute error      6 22
Adams — Bashforth      371 581
Adams — Bashforth-type predictors      404
Algorithms      1
Algorithms, instability of      378
Aliasing      14 505 514 515 531 551
Analysis of variance      118
Analytic substitution      10 229 244 549 632
Approximation of singularities      649
Ascending factorials      162
Backward analysis      54
Backward differences      162
Bairstow’s method      108
Bairstow’s method, convergence of      110
Band-limited functions      15 551 552 557
Bergland, G. P.      543
Bernoulli numbers      188—189 208
Bernoulli numbers, by generating function      188—189 197
Bernoulli, J.      188
Bessel, F. W.      451
Bessel’s inequality      451 507
Bessel’s interpolation formula      306 309
Bickley’s formula for integration      316
Binary representation of numbers      29
Binary representation of numbers, conversion      30
Binary representation of numbers, conversion, nonunique      32
Binomial coefficient $C(N, k)$      152
Birkhoff interpolation      287
Birkhoff, G. D.      287
Bisection method for zeros      62
Bode’s integral      651
Buffon, G. L.      134
Buffon, G. L., needle      134
Businger, P. A.      686
Central differences      163
Chebyshev approximation, calculation of coefficients      486
Chebyshev approximation, calculation of coefficients, from an integral      488
Chebyshev approximation, calculation of coefficients, from differential equation      492
Chebyshev approximation, Lanczos’ tau process      490
Chebyshev approximation, Lanczos’ tau process, rational function      498
Chebyshev criterion      477
Chebyshev design for differential equations      585
Chebyshev design for differential equations, details of      587
Chebyshev evaluation      493
Chebyshev integration      326 330
Chebyshev measure of linear independence      683
Chebyshev polynomials, definition      470
Chebyshev polynomials, definition, derivatives of      479
Chebyshev polynomials, definition, discrete      472
Chebyshev polynomials, definition, from power series      474
Chebyshev polynomials, definition, orthogonality      470
Chebyshev polynomials, definition, products of      476
Chebyshev polynomials, definition, shifted      481
Chebyshev smoothing      571
Chebyshev, P. L.      470
Code of ethics      707 709
Completeness      451
Completeness of finite Fourier series      513
Complex frequencies      634
complex numbers      54
Complex numbers, quadratic factors      54
Complex zeros      106
Dawson’s integral      651
Defining equations      251 256 273 280 282 287 289 312 318 320 322 323 326
Definite integrals      339
Delta$ operator      149
Demoivre, A.      470
derivatives      565 599
Derivatives, use of      10
Descending factorials      157
Design of Experiment      658
Difference equations      211 583
Difference operator      149
Difference table      153
Difference table, error propagation in      169
Different time constants      422
Differential equations      379 393
Differential equations, numerical solution of      382
Differential equations, systems of      391
Digamma function      208
Digital filters      17 592
Direct method      248 256 280
Direction field      380
Distribution, of mantissas      32
Distribution, of mantissas of products      35
Divided differences      298
Divided differences, table      299 301
Duke, Anne      294
Economization      484 485
Eigenvalues      686
Eigenvalues, real      689
Eigenvectors      686
Eigenvectors, orthogonality      689
Elliptic integrals      54
Epstein, M. P.      291 686
Equally spaced sampling      505
Error in table      179
Error integral      193
Error integral, table of      177
Error terms, Fourier series      519
Error terms, polynomial      258
Errors, isolated      178
Euler — Maclaurin formula      208 346
Euler’s constant      136 208
Euler’s method for differential equations      382
Euler’s method for differential equations, modified      641
Euler’s method of summation      201
Everett’s interpolation formula      309 443
Exact matching      9
Exponential approximation      616
Exponential approximation, known exponents      616
Exponential sums      616
Factorial notation      157
False position      64
False position, modified      65
Fast Fourier Transform      539
Feedback      5 358
Fejer summation      536
Fibonacci (Leonardo of Pisa)      215
Fibonacci numbers      215
Filters      568 575
Filters, differentiating      599
Filters, digital      592
Filters, nonrecursive      593
Filters, recursive      601
Finite difference calculus      8 146
Finite Fourier series      510
Finite Fourier series, relation to continuous      513
Finite Fourier series, twelve-point      544
Finite sample size effects      561
fixed-point numbers      20
Fletcher — Powell method      671
floating-point numbers      21
Folding frequency      514
Forsythe, G. E.      131 460
Fourier approximation      13 503
Fourier coefficients      447
Fourier integral      15 548 554 573
Fourier series      13 445 503
Fourier series, complex form      509
Fourier series, continuous      507 549
Fourier series, convergence      527
Fourier series, differentiation of      538
Fourier series, finite      510
Fourier series, integration of      520
Fourier series, local      546
Fourier series, poor man’s      612
Fourier series, relation to finite      513
Fourier series, unknown exponents      620
Fourier transform      551
Fourier transform, numerical evaluation of      639
Fourier transform, pairs of      555
Fourier, J. B. J.      447
Fowler, M. E.      422 642 643
Fox, Leslie      426
Functions of two variables      97
Gauss elimination      113
Gauss elimination, discussion of      126
Gauss elimination, failures of      120 122 124—125
Gauss integration      317
Gauss integration formal      322
Gauss integration, analysis      323
Gauss integration, error term      325
Gauss integration, special cases      327
Gauss integration, using derivatives      334
Gauss interpolation formula      306
Gauss quadrature zeros      457
Gauss — Jordan elimination      116 129
Gauss, C. F.      113
Generating functions      186
Gibbs phenomenon      532
Gradient      665
Gradient, estimation of      669
Gradient, following      667
Graphical solution of differential equations      60
Gray code      604
Gregory formula      310 314 315 347
Gregory, James      310
Half Simpson formula      254
Hand calculation errors      39—40
Hermite interpolation      278
Hermite polynomials      457
Hermite, Charles      278
Hermitian matrix      688
Herschel, Sir J. F. W.      432
Hessenberg form of a matrix      689
Hilbert determinant      439
Hilbert, D.      439
Hopkins, I. L.      376
Householder transformation      693
Householder, A. S.      627
Ill-condition, matrix      121
Ill-condition, matrix, minimum      658
Ill-condition, matrix, right-hand side can cause      125
Ill-condition, matrix, systems      121
Improved search      90 93
Indefinite integrals      357
Infinite series      192
Influence function, constant sign      264
Influence function, constant sign, nonconstant sign      269
Influence function, constant sign, polynomial      262
Instability in algorithms      378
Integral equations      164 199
Integrals, indefinite      357
Integration      566 575
Interpolation, error in      236
Interpolation, in tables      303
Interpolation, Lagrange      235
Interpolation, periodic functions      516
Interpolation, polynomial      226
Invariance principle      101
Invariance principle, applied to polynomials      101
Invariance principle, applied to power spectra      516
Invariance principle, applied to simultaneous equations      118
Invariant algorithm      7 72 670
Invert problem      363 367
Isolated errors      178
Jacobi, C. G. J.      363
Jansson, B.      145
Kaiser, J. F.      602
Kaplan      637 639
Kernel      519
Kernel, modified      519
Knuth, D.      145
Kopal, Z.      414
Krylov, V. I.      635
Kummer, E.      195
Kummer’s melhod      195 200
Kuo, F. F.      602
Lagrange interpolation formula      551
Lagrange multipliers      662 675
Lagrange, J. L.      235
Laguerre polynomials      457
Laguerre, E. N.      457
Lanczos’ sigma factors      534 535 538
Lanczos’ tau process      490
Laplace transform      628
Le Page, W. R.      629
Leading digits      6 34
Least squares, with constraints      467
Least squares, with constraints, faults of      469
Least squares, with constraints, fitting of, exponentials      623
Least squares, with constraints, fitting of, nonpolynomial      441
Least squares, with constraints, fitting of, polynomials      437
Least squares, with constraints, fitting of, rational functions      497
Least squares, with constraints, fitting of, straight line      435
Least squares, with constraints, Fourier coefficients      450
Least squares, with constraints, measure of linear independence      682
Least squares, with constraints, practice      429
Least squares, with constraints, simultaneous equations      700
Least squares, with constraints, smoothing      468 570
Least squares, with constraints, theory      427
Legendre polynomials      455
Legendre, A.      455
Linear equations      112 678
Linear independence      677
Linear independence and orthogonality      448
Linear independence and sampling      680
Linear independence of eigenvectors      687
Linear independence of exponentials      618
Linear independence of powers of x      682
Linear independence, Chebyshev measure      683
Linear independence, least squares measure      682
Linear programming      674
Lobatto integration      328
Lozenge diagram      304
Matrix inversion      128—129
Maximum and minimum      659
Maximum and minimum, example      660
Maximum and minimum, in two variables      660
Mean      28
Mean value theorem      49
Mean Value Theorem for Integrals      70
Median      431
Method of zeros and poles      640
Midrange      431
Milne-type predictors      402
Minimax criterion      478
Modified false position      65
Moler, C. B.      686
Moments      251
Moments, all zero      326
Monte Carlo method      133
Monte Carlo method, value of $1/e$      135
Monte Carlo method, value of $\gamma$      136
Monte Carlo method, value of $\pi$      134
Moore, R.      167
Motto      3 11 703
Multiple zeros      98
Multiple zeros, complex      84 95 103 111
Multiple zeros, real      104
Newton expansion      158 165
Newton interpolation formula      29
Newton interpolation formula forward      305
Newton interpolation formula, backward      305
Newton interpolation formula, equally spaced      302
Newton — Cotes formulas      342
Newton’s method      68
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