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| Авторизация |
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| Buckingham R.A. — Numerical Methods |
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| Предметный указатель |
Adjoint matrix 358 373 420
Airy’s equation 183 215 236
Aitken, A.C. 93 102 262 272 277 312 319 389 401 586
Aitken’s  process 260 283 393 430
Algebraic (transcendental) equations, roots of, by Newton — Raphson method 250 253
Algebraic (transcendental) equations, roots of, by “false position” 249
Algebraic (transcendental) equations, roots of, close and multiple roots 254 295
Algebraic (transcendental) equations, roots of, complex roots 266
Algebraic (transcendental) equations, roots of, simultaneous equations 262 (see also “Polynomial equations”)
Algebraic equations, linear 336
Algebraic equations, linear, conditions for solution 336
Algebraic equations, linear, elimination without division 356
Algebraic equations, linear, escalator method 357
Algebraic equations, linear, Gauss — Doolittle method 339 343
Algebraic equations, linear, ill-conditioned equations 362 444
Algebraic equations, linear, improvement of solution 359
Algebraic equations, linear, matrix resolution 343 352 368
Algebraic equations, linear, matrix-squaring method 427
Algebraic equations, linear, minimized iterations 357 413
Algebraic equations, linear, orthogonal vectors, use of 357
Algebraic equations, linear, pivotal condensation 356
Algebraic equations, linear, residual errors 342 355 359
Algebraic equations, linear, Seidel’s iterative method 423
Algebraic equations, linear, square-root method 344
Algebraic equations, linear, triangular equations 337
Algebraic equations, linear, unsymmetrical equations 351 354
Allen, D.N.de G. 523 566
Alternating series 161
Amplitude and phase method 194 201
Anderson, R.L. 323 583
Arc tan x, tabulation of 162 204
Asymptotic series 188 et seq.
Babbage, W. 32
BaggoU, E.A. 174 244
Bairstow, L 9 274
Banachiewicz, T. 344
Bateman, E.27. 295 296
Bemouilli — Aitken method 277 394
Bemouilli, D. 277
Bessel*s interpolation formula 111 114 116 119 123 147 574
BessePs equation 171 186 193 222 240
BicUey, W.D. 126 155 166 458 508 580 532
Biharmonic equation 514 565
Birge, B.T. 312 314 323 389 583
Birkhoff, G.J.D. 507
Bite, W. 478
Black, A.JV. 339 346
Blanch, Gertrude 421
Bodewiq, E. 255 258 285 295 296
Boole, G. 80
Boole’s rule 80 87 88 89 219 498
Booth, A.D. 41
Boundary conditions for ordinary differential equations 173 197
Boundary conditions for partial differential equations 512 563
Boundary conditions, involving derivatives 453
Boundary conditions, two-point 240 446
Bowden, B.V. 41
Brillouin, L. 207
Brodetsky, S. 292
Bromwich, T.J.I’A. 188
Brooker, B.A. 266
Brown, S.L. 276
Brunt, D. 329
Bush, V. 43
Calculating machines 32
Calculating machines, analogue machines 43
Calculating machines, cinema-integraph 44
Calculating machines, desk calculators 33
Calculating machines, electronic digital computers 42
Calculating machines, harmonic synthesizer 276
Calculating machines, isograph 276
Calculating machines, National accounting machine 32 41 122
Calculating machines, punched card machines 41
Calculating machines, relay computers 42
Calculating machines, slide-rules 32
Calculations, unit 36
Characteristics of partial differential equations 511
Chebyshev polynomials 120
Chevilliet 88
Clemence 16
Clenshaw, C.W. 209 217
Cofactors 357 373
Collar, A.R. xi 246 392 420 432 445 477
Collatz, L. xi 466 476 478
Complex variable, functions of 507
Comrie, L.J. 29 32 123 484
Cooper, J.L.B. 458
Cosen, C.R. 31
Cosine integral 191
Cotes, B. 79
Coulomb functions 196
Courant, R. 459 526
Cowell, P.H. 226
Crandall, S.H. 514
Crank, J. 516 520
Cross-means 102
Crout, P.D. 471 475
Cubature 493
Cubic equations 264
Curve-fitting 299
Curve-fitting, Aitken’s method 319
Curve-fitting, by exponentials 329
Curve-fitting, orthogonal polynomials, use of 312
Curve-fitting, straight-line fitting 315 (see also “Least squares”)
Dandelin, Q.P. 285
Danielewsky, A. 375 389
Darby, P. 542
Darwin, C.G. 201
Davis, H.T. 115 323
Decimal rounding notations 5
Descartes’ Rule of Signs 246
Determinants equations 294 370
Determinants equations, companion matrix 375
Determinants equations, comparison of direct expansion methods 391
Determinants equations, Danielewsky’s method 375
Determinants equations, fitting by polynomials 389
Determinants equations, Frobenius standard form 374
Determinants equations, Lanczos’ method 382
Determinants equations, Samuelson’s method 379 (see also “Latent roots of matrices”)
Determinants, evaluation of 357
Dietzold, R.L. 394
Difference equations, solution of 233 260 534
Differences 26 46
Differences, backward (ascending) 48
Differences, central 50
Differences, forward (descending) 46
Differences, mean 51
Differences, modified 119 484
Differences, of factorials 53—56
Differences, relations with tabular values 48
Differences, short notation for 51
Differences, tables of 26
Differential equations, nonlinear second-order equations, comparison of methods 232
Differential equations, nonlinear second-order equations, comparison of methods, numerical integration 216 220 226 230
Differential equations, nonlinear second-order equations, comparison of methods, two-point boundary conditions 242
Differential equations, ordinary 169—245 446—463
Differential equations, ordinary, first-order equations, numerical, integration of 209 217 224 236 238
Differential equations, ordinary, linear second-order equations, amplitude and phase method 194 201
Differential equations, ordinary, linear second-order equations, boundary conditions 173 197
Differential equations, ordinary, linear second-order equations, general solution 175
Differential equations, ordinary, linear second-order equations, latent roots 241 458 526
Differential equations, ordinary, linear second-order equations, normal form 170
Differential equations, ordinary, linear second-order equations, numerical integration 212 227
Differential equations, ordinary, linear second-order equations, solution near regular singularity 185
Differential equations, ordinary, linear second-order equations, Stokes’ solution 191
Differential equations, ordinary, linear second-order equations, two-point boundary conditions 240 453 458
Differential equations, partial 510—567
Differential equations, partial, boundary conditions 512
Differential equations, partial, characteristics 511
Differential equations, partial, classification 510 (see also “Elliptic” “Hyperbolic” “Parabolic
| Differential equations, series solutions, asymptotic series 188
Differential equations, series solutions, perturbation method 197
Differential equations, series solutions, Picard’s method 180 (see also “Latent roots” “Relaxation “Integration step-by-step” “INDEX
Differential equations, series solutions, Taylor series 176
Differential equations, WKB (Jeffreys method) 199
Differentiation, numerical,  ,  operators 502 505
Differentiation, numerical, by central differences 127 152
Differentiation, numerical, by forward and backward differences 126
Differentiation, numerical, errors of 85
Differentiation, numerical, Lagrangian 77 579
Differentiation, numerical, partial 502
Dimsdale, B. 277
Divided differences 92—107
Divided differences, definitions 92
Divided differences, interpolation formulas, construction of 98
Divided differences, linear cross-means 102
Divided differences, Newton’s polynomial expansion 95
Divided differences, quadratic cross-means 104
Domb, C. 256
Doolittle, M.H. 339
du Fort, E.C. 514 518
Dunvan, W.J. xi 246 270 274 296 392 432 445 477
Dwight, H.B. 115
Dwyer, P.S. xi 344 356—357
Echert, C.J. 41
Eider, L. 157 161
Eigenvalues see “Latent roots”
Elliptic partial equations 533—565
Elliptic partial equations, 4- and 9-point blocks, use of 549
Elliptic partial equations, boundary conditions 513
Elliptic partial equations, curved boundaries 554 558
Elliptic partial equations, definition 511
Elliptic partial equations, difference equations, analytical solution of 535
Elliptic partial equations, diffusion equation, use of 538
Elliptic partial equations, finite difference approximations 533
Elliptic partial equations, improvement of solutions 558
Elliptic partial equations, Liebmann — Richardson method 539
Elliptic partial equations, numerical examples 536 545 552 554
Elliptic partial equations, relaxation method 550
Elliptic partial equations, Shortley — Weller method 542
Emde, P. xii 265
Encke, J.P. 133
Error of cubature 508
Error of differentiation 85 128 579
Error of extrapolation 113
Error of interpolation 19 22 84 118 574
Error of quadrature 82 85 87 135 576 580
Error of step-by-step integration 215 218 229 233
Errors 2—12
Errors, combination of 7
Errors, computational (truncation) 7
Errors, definitions of 2
Errors, detection of, by differencing 25
Errors, experimental 6
Errors, normal distribution of 7
Errors, principle of equal 10
Errors, rounding 3 18 22 136 215 360
Errors, standard deviation of 7 11 314
Euler formulas 157
Everett’s interpolation formula 112 114 120 122 147 488
Exponential integrals 195 205
Extrapolation to zero interval 90 365 455 462 468 558
Eyres, N.R. 523
Factorials 52—67 113 568
Factorials, addition theorems for 54
Factorials, ascending and descending 52
Factorials, central 54
Factorials, differences and sums of 53 56
Factorials, expansion of, in powers 568
Factorials, inverse 53 54
Factorials, mean central 55
Factorials, reduced 52 56
False position, method of 249
Feller, W. 402 421
Fisher, R.A. 323 583
Flanders, D.A. 565
Fletcher, A. xii
Flocquet’s theorem 207
Forsythe, G.E. 402 421 423 443
Fourier analysis 328
Fox, L. 205 209 233 240 244 354 356 357 368 437 455 558 565
Frame., J.S. 276 420
Frankel, S.P. 514 518
Frazer, R.A. xi 246 270 274 296 432 445 477
Fredholm integral equations 463—478
Fredholm integral equations, collocation 477
Fredholm integral equations, Grout’s method 471
Fredholm integral equations, iterative solution 464
Fredholm integral equations, latent roots of 463 469 473
Fredholm integral equations, method of least square error 477
Fredholm integral equations, numerical examples 467 469 473 475
Fredholm integral equations, summation method 466
Fredholm integral equations, variational method 478
Fresnel integrals 191
Fried, B. 542
Fry, T.C. 276
Functions of complex variable 507
Gamble, E.H. 542
Gauss interpolation formulas 99 110 114
Gauss quadrature formulas 133 135—138 576—578
Gauss transformation 441
Gauss — Doolittle method 339
Gauss, C.P. 133 423 437 443
Gerlvng, C.L. 423
Goodwin, E.T. 209 233 240 244 368
Gordon, A.P. 180
Graduation 299 333—334
Graeffe, C.H. 285
Green, G. 201
Green’s function 464 471
Green’s type (WKB) solutions 199
Gregory, J. 108
Guarding figures, use of 14 18 213 360
Harmonic analysis 327
Hartley, H.O. 79 91
Hartree, D.P. xi 41 123 139 154 236 256 403 502 512 523
Hayes, J.G. 354
Herget, P. 16
Hermite polynomials 325
Hestenes, M.R. 356 357
Horner’s root-shift 253 274
Hotelling, H. 392 401 428 432
Houseman, E.E. 323 583
Huskey, H.D. 356
Hyman, M.A. 514 537
Hyperbolic partial equations 525
Hyperbolic partial equations, boundary conditions 513
Hyperbolic partial equations, definition 511
Hyperbolic partial equations, d’Alembert’s solution 512
Hyperbolic partial equations, finite difference approximation 525
Hyperbolic partial equations, importance of characteristics 512
Hyperbolic partial equations, use in evaluating latent roots 526
Ince, E.L. 192
Indicial equation 185
Integral equations 206 362 463
Integration see “Quadrature” “Cubature”
Integration, step-by-step, integral methods, using differences 224
Integration, step-by-step, integral methods, without differences 217
Integration, step-by-step, parabolic equations 616
Integration, step-by-step, recurrence methods 209
Integration, step-by-step, Taylor series methods 178 236 ordinary”)
Interpolation 69 108 481
Interpolation, by cross-means 102
Interpolation, by divided differences 100
Interpolation, by ordinary differences 108
Interpolation, inverse 73 123
Interpolation, inverse, by Newton’s polynomial 106
Interpolation, inverse, by successive approximation 123
Interpolation, inverse, Lagrangian 73
Interpolation, inverse, possible dangers of 74
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