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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:

This book is written for scientists and engineers who expect to use modern large-scale digital computers as a tool for research and development and as a text for advanced undergraduate-level courses in numerical analysis. It is the author's belief that they do not need a book of formulas or a collection of isolated results but rather an organized presentation of the main ideas in the computing field so that they can understand what relation the numbers computed by a machine bear to a particular problem. As the motto of the book states, it is insight, not numbers, that is being sought.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1962

Количество страниц: 427

Добавлена в каталог: 12.07.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Gamma$ function, table of      32
$\sigma$ factors      297 298 300
$\tau$ process      258 260
Abramowitz, M.      56 164
Adams — Bashforth method      210
Adams — Bashforth method, indefinite integration      177
Adams — Bashforth method, predictor      204
Adams — Bashforth method, transfer function      328
Adams — Bashforth method, type predictors      203
Algorithms      351
Alias and alibi      5 241
Aliasing      276 303
Aliasing, of Fourier coefficients      278
Analytic substitution      81 83
Archimedes      394
Ascending factorials      22
Ashenhurst, R. L.      26
Asher, M.      245
Backward differences      22
Bairstow’s method      356
Band-limited function      4 303 308
Barycentric formula      95
Benford, F.      40
Bessel functions      56 285 333 335
Bessel’s inequality      70 236
Bessel’s interpolation formula      113 116
Binomial coefficients      8 111
Bisection method      352 355
Blackman, R. B.      318
Boefinger, E.      388
Boefinger, V. J.      388
Buffon Needle Problem      390 393
Central differences      22
Central-limit theorem      34 228 387
Change of scale effects      162
Chebyshev criterion      88 252 323
Chebyshev design      337
Chebyshev design, of filters      332 334
Chebyshev integration      135 284
Chebyshev polynomials      108 249
Chebyshev polynomials, shifted      257 261
Chebyshev, an identity      333
Chebyshev, spelling of      88 250
Class of functions      86
Completeness      236
Completeness, of Fourier series      69—70
Comrie      116
Conditional stability      175
Construction of polynomials      96
Convolution theorem      310
Coveyou, R. R.      387
Dawson’s integral      344
Debye, P.      395
Defining equations      124 131 169 339
Definite integrals      153
Delta$ operator      6
Delta$ operator, iterated      7
Derivative estimate from two points      127 318
Design of Experiment      86 393
Determinant method      93 124
Difference correction      222
Difference operator      5
Difference table, check      9
Difference table, construction by      10
Difference table, construction by, table      11
Difference, of miscellaneous functions      7
Difference, of product      6
Difference, of quotient      6
Difference, repeated      7
Differencing      5
Differential equations      183 194 211 331
Differential equations, higher derivatives      216
Differential equations, linear, with constant coefficients      217
Differential equations, numerical example      187
Differential equations, singularity in      344
Differential equations, solution of      183
Differential equations, solution of, starting      186
Differentiating      318
Digamma function      57
Direction field      184 193
Divided differences      98
Divided differences, table of      99
Divided differences, table of, alternative form      101
DOUBLE PRECISION      25 205 364
Doubling the interval      208
Dynamic programming      375
Economization      253
Economization, mechanization of      255
Eigenvalues of matrices      367
Elliptic integrals      284
Equi-error lines      172
Ergodic theory      29
Error integral      48 158
Error integral, table of      111
Error propagation, single error in a table      10
Error propagation, table of      12
Error term, order of      143
Error, of Hermite interpolation      104
Error, of periodic functions      282
Error, of polynomial interpolation      102
Euler — Maclaurin formula      57 140
Euler’s constant      57
Euler’s method, for differential equations      186
Euler’s method, of summation      50
Everett’s formula      116
Exponential approximation      338
Factorial functions      14
Factorial functions, negative exponents      15
Failure of polynomial approximation      94
Feedback      165
Fejer summation      298
Fibonacci numbers      62
Filon’s method      319
Filters      313
Filters, smoothing      314 317
Finite difference equations      60
Finite Fourier series      67
Finite Fourier series, coefficients of      68
Finite Fourier series, coefficients of, computation of      71—76
Finite Fourier series, completeness of      69
Finite Fourier series, cosine expansion of      76
Finite Fourier series, error of      71
Finite Fourier series, local series      77
Finite sample size      311
Floating-point mode      4
Folding frequency      280 303
Forsythe, G. E.      ix x 245
Fourier approximation      275
Fourier coefficients      68 233
Fourier coefficients, aliasing of      278
Fourier coefficients, and least squares      237
Fourier integral      301
Fourier integral, derivation of      306
Fourier series      278
Fourier series, complex number representation      302
Fourier series, convergence of      290
Fourier series, convergence of, improving      293
Fourier series, modified kernel      282
Fourier series, orthogonality      67
Fourier transform      303 306
Fox, L.      117 222
Fundamental polynomials      125
Fundamental theorem of difference calculus      8
Furry, W. H.      40
Gauss elimination method      360
Gauss interpolation formula      113
Gauss interpolation formula, two-point      122
Gauss quadrature      121 130 160
Gauss quadrature, error of      161
Gauss quadrature, error of, change of scale      163
Gauss — Chebyshev integration      160
Gauss — Hermite integration      160
Gauss — Jordan elimination      362
Gauss — Laguerre integration      160
Gauss — Legendre integration      160
Gauss — Seidel method      363
Gaussian integration      284
General integration formula      168
Gibbs phenomena      295
Gilbert, E. N.      388
Givens, W. A.      369
Goertzel, G.      72
Goudsmit, S. A.      40
Gray, L. H.      26
Gray, M. C.      56
Green, B.      388
Gregory integration formula      57 138 158
Gregory integration formula, derivation of      138
Gregory integration formula, Lagrange form      140
Gregory integration formula, summation of series      162
Gregory integration formula, use of      158
Half — Simpson formula      127 167 178
Halton, J. H.      120
Halving interval      208
Hammersley, J. M.      393
Hamming, R. W.      177 181
Harrison, J. C.      26
Hastings, C., Jr      389
Hermite interpolation      96 122
Hermite interpolation, error of      104
Hermite interpolation, inverse matrix for      129
Hermite polynomials      56 240
Hermite-type formulas      128
Heuristics      351
High-accuracy predictor      204
Hilbert determinant      230
Hildebrand, F. B.      117 271
Hopkins, I. L.      181
Householder, A.      342 366 369
Hurwitz, H.      40
Influence function      144 196 202
Influence function, constant sign      147
Influence function, for general integration formula      169
Influence function, nonconstant sign      149
Influence function, region of validity      170
Information regeneration      119
Instability      165 180 190
Integral equation      181 275
Integrals, indefinite      165
Integration formulas      167
Integration formulas, for periodic functions      284
Interpolation of periodic functions      280
Interpolation of periodic functions, from universal matrices      128
Interpolation of periodic functions, in a table      110
Inventory simulation      375
Isolated error      10
Isolated error, location in a table      30
Isolated error, table of      12
Klem, L.      388
Kopal, Z.      117 161
Kronecker delta function      23
Kummer’s method      48
Lagrange form of difference      13
Lagrange interpolation      94 304
Lagrange interpolation, cubic, coefficients for      115
Laguerre polynomials      56 240
Lanczos $\sigma$ factors      297
Lanczos $\tau$ process      258 260
Lanczos differentiation technique      300
Lanczos, C.      253 258 260 342
Lanczos’ $\sigma$ method      300
Laplace transform      341
Least squares      223
Least squares, polynomial fitting by      229
Least squares, practice of      244
Least squares, principle of      224
Least squares, theory of      223
Least squares, with restraints      242
Least-significant-digit theory      33
Legendre polynomials      56 240
Levy, Milton      x 384
Lighthill, M. J.      301
Linear differential equations      214
Linear independence      234
Linear interpolation for a zero      353
Linear operator      6 83
Linear programming      375
Linear restraints on integration formulas      135
Lin’s method      356
Lobatto integration      132
Lozenge diagram      111
Lozenge diagram, figure      112
Lozenge diagram, rules      112
Machine errors      209
Maclaurin integration formulas      160
Maclaurin integration formulas, exercise involving      140
Maclaurin integration formulas, three-point      124
Matching moments      262
Matrix inversion      366
Mean differences      22
Median value      225
Metropolis, N. C.      26
Midpoint formula      167
Midpoint integration      120
Midrange value      226
Milne method of integration      179
Milne type predictors      202
Milne — Thomson, L. M.      271
Milne, W. E.      179 205 268 271
Mineur, H.      161
Minimax principle      252
Missing values      13
Modified kernel      282
Modify      192 206 207 214
Moments, $m_{k}$      124 286 288 339
Monte Carlo methods      390
Mop up      186 192 206
Morton, K. W.      393
Moshman, Jack      388
Most-significant-digit theory      35
Most-significant-digit theory, table of distribution      36
Most-significant-digit theory, table of distribution, of product      37
Most-significant-digit theory, table of distribution, of quotient      37
Most-significant-digit theory, table of distribution, of sum      38
Motzkin, T.      17
Muller, D.      356
Newton — Cotes formulas      156 284
Newton’s backward formula      113
Newton’s interpolation formula      15 97 110 112
Newton’s method for zeros      81 355
Newton’s method for zeros, extended      82
Newton’s method for zeros, two dimensions      357
Noise amplification      28
Noise amplification factor      29
Noise amplification factor, in a table      28
Noise amplification factor, in Newton — Cotes formulas      154
Noise correlation      29
Noise correlation, in a table      27 30
Nonlinear transformation      54
Nonperiodic functions      301
Nordsieck, A.      207
Normal curve      263
Normal distribution      34
Normal distribution, of random numbers      389
Normal equations      229
Normal error      263
Normal law, derivation of      226
Numerical integration of linear equations      214
Numerov’s method      215
Nyquist frequency      280 303
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