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| Авторизация |
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| Hamming R.W. — Numerical Methods For Scientists And Engineers |
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| Предметный указатель |
 function, table of 32
 factors 297 298 300
 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 factors 297
Lanczos process 258 260
Lanczos differentiation technique 300
Lanczos, C. 253 258 260 342
Lanczos’ 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,  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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