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| Demidovich B.P., Maron I.A. — Computational Mathematics |
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| Предметный указатель |
Even-digit rule 26
Exact methods 273
Exact number 19
Exhaustion, method of 443 444
Expansion of secular determinants 410ff
Expansion of secular determinants, comparison of different methods of 429
Expansion, bilinear (of a matrix) 392
Expansion, Stirling's 207
Exponential functions 50 91
Exponential functions, computing values of 91
Extrapolation 519
Extrapolation, backward 529
Extrapolation, forward 529
Extrapolation, Richardson 622f
Extremal property of eigenvalues 387
Factorial(s) 517 see
Factorial(s), inverse 205
Faddeyev, D.K. 272 321 458 657
Faddeyeva, V.N. 272 321 335 393 409 458 573 675
Fikhtengolts, G.M. 54 76 114 161 228 648 675
Final check 17
Finite differences 507ff
Finite-difference operator 628
Form(s), bilinear (of a matrix) 384
Form(s), computing 16
Form(s), Frobenius standard 412
Form(s), quadratic 311 see
Formula(s) for central derivatives 580
Formula(s) for interpolating to halves 536
Formula(s) of approximate differentiation, based on Newton's first interpolation formula 575
Formula(s) of approximate differentiation, based on Stirling's formula 580
Formula(s), Bessel's interpolation 534 535
Formula(s), Bessel's, for parabolic interpolation 535
Formula(s), Cardan's 186
Formula(s), central 580
Formula(s), central interpolation 552
Formula(s), central-difference 531
Formula(s), Chebyshev's quadrature 607ff
Formula(s), Cramer's 276
Formula(s), cubature 590 641ff
Formula(s), cubature of Simpson type 644
Formula(s), cubature, Simpson's 644
Formula(s), empirical 524
Formula(s), Euler — Maclaurin 628 630
Formula(s), Euler — Maclaurin summation 630
Formula(s), Gauss' quadrature 611 614
Formula(s), Gaussian interpolation 531 532 533
Formula(s), general trapezoidal 601
Formula(s), Lagrange's interpolation 539 541
Formula(s), Lambert's 100
Formula(s), Markov's 566
Formula(s), Newton — Cotes (of higher orders) 599
Formula(s), Newton — Cotes quadrature 593
Formula(s), Newton — Leibniz 590
Formula(s), Newton's first interpolation 519 522
Formula(s), Newton's quadrature 599
Formula(s), Newton's second interpolation formula 526 527
Formula(s), quadrature 590
Formula(s), quadrature of closed type 591
Formula(s), quadrature of open type 591
Formula(s), quadrature, accuracy of 618
Formula(s), quadrature, Newton's 599
Formula(s), Simpson's (and its remainder term) 596
Formula(s), Simpson's general 603
Formula(s), Stirling's interpolation 533
Formula(s), trapezoidal (and its remainder term) 595
Forsythe, G.E. 321
Forward extrapolation 529
Forward interpolation 529
Forward substitution 280 see
Fourier coefficients 213
Fourier coefficients, estimates of 213
Fourier trigonometric series 213
Fourier, theorem of Budan — Fourier 175 176
Fraction(s), continued 55 see
Fraction(s), rational 82 see
Frazer, R.A. 272 675
Frobenius matrix 412 415 418
Frobenius standard form 412
Fuks, B.A. 202 675
Function(s), analytic 89
Function(s), Bessel's (of order zero) 582
Function(s), computing values of 77ff
Function(s), distribution 651
Function(s), exponential 50 91
Function(s), hyperbolic 101
Function(s), interpolating 518
Function(s), interpolation of 507ff 519
Function(s), iteration for approximating the values of 103ff
Function(s), jump 221
Function(s), logarithmic 95
Function(s), signum 86
Function(s), trigonometric 49 98
Function(s), zero of 115
Fundamental system of solutions 365
Fundamental theorem of algebra 162
Gantmacher, F.R. 393 675
Gauss' first interpolation formula 532
Gauss' quadrature formula 611 614
Gauss' second interpolation formula 532 533
Gaussian interpolation formulas 531 532 533
Gaussian method 277ff
Gaussian method, inversion of matrices by 290
Gaussian method, use of in computing determinants 288
Gaussian random sequence 652
Gavurin, M.K. 458 676
Gavurin, method of 458
Gelfand, I.M. 393 458 676
Gelfond, A.O. 161 202 228 676
General formula for errors 42
General trapezoidal formula 601
Generalized power 517
Generate 342 see generated
Gnedenko, B.V. 674 676
Goncharov, V.L. 573 676
Gradient (of a function) 497
Gradient method 496
Graeffe 182
Graeffe, method of Lobachevsky — Graeffe 179 182
Graphical differentiation 586
Graphical integration 639
Graphical solution of equations 119
Grave, D. 202 676
Halving method 121
Hermitian symmetry 343
Hero's algorithm 107
Hero's process 107
Hildebrand, F.B. 201 202 676
Horizontal difference table 511
Horner's scheme 77 78
Horner's scheme, generalized 80—82
Householder, A.S. 393 506 674 676
Hua's Theorem 179
Hurwitz conditions 405
Hurwitz theorem 406
Hyperbolic cosine 101
Hyperbolic functions 101
Hyperbolic sine 101
Hyperbolic tangent 102
Hypercube, unit m-dimensional 656
Identical transformation 375
Improper integral(s) 633
Improper integral(s), approximation of 633
Improving roots 284
Inequality, Bessel 216
Inequality, Cauchy 245
Infinite continued fraction 55
Initial basis of a space 341
Initial error 23
Integral(s), convergent 633 635
| Integral(s), divergent 633 635
Integral(s), improper 633
Integral(s), multiple 656
Integral(s), probability 561
Integral(s), proper 633
Intergation, approximate 590ff
Intergation, graphical 639
Intermediate check 17
Interpolating function 518
Interpolating to halves, formula for 536
Interpolation 519
Interpolation formula(s) with constant interval (general) 536ff
Interpolation formula(s), Bessel's 534 535
Interpolation formula(s), Bessel's, remainder term of 552
Interpolation formula(s), central 552
Interpolation formula(s), error estimate of 547
Interpolation formula(s), Gauss' first 532
Interpolation formula(s), Gauss' second 533
Interpolation formula(s), Gaussian 531
Interpolation formula(s), Lagrange's 539 541
Interpolation formula(s), Newton's 519
Interpolation formula(s), Newton's first 519 522
Interpolation formula(s), Newton's second 526 527
Interpolation formula(s), Newton's, error's estimates of 550
Interpolation formula(s), Newton's, for a function of two variables 571
Interpolation formula(s), Newton's, for unequally spaced values of the argument 556 558
Interpolation formula(s), Stirling's 533
Interpolation formula(s), Stirling's, remainder term of 552
Interpolation in the narrow sense 519
Interpolation method, for expanding a secular determinant 565
Interpolation of functions 507 519
Interpolation of functions of two variables 567
Interpolation points 518
Interpolation points, best choice of 553
Interpolation, backward 529
Interpolation, forward 529
Interpolation, method of 411
Interpolation, parabolic 522
Interpolation, problem of (statement of) 518
interval 507 see
Interval, variable 555
Invariance of a linear subspace 379
Inverse factorials 205
Inverse interpolation for case of equally spaced points 559
Inverse interpolation for case of unequally spaced points 562
Inverse interpolation, finding roots of an equation by 564
Inverse matrix 236
Inverse matrix, correcting elements of an approximate 316ff
Inverse matrix, properties of 239
Inverse problem of theory of errors 44
Inverse problem of theory of errors, second 48
Inverse transformation 373
Inverse, additive (of a matrix) 232
Inversion of matrices 236
Inversion of matrices by Gaussian method 290
Inversion of matrices, isolation, of roots 115
Inversion of matrices, isolation, of singularities bv Kantorovich method 635
Inversion of matrices, solution of systems of linear equations by 273
Iteration see "Linear system"
Iteration for approximating the values of a function 103ff
Iteration of a vector 431
Iteration processes, convergence of (for systems of linear equations) 322ff 394ff
Iteration processes, estimate of the error of approximations in 324
Iteration, method of 138ff 300 302 484ff
Iteration, process of, convergence of 491 493 see
Iterative methods see "Methods of iteration"
Jacobi matrix 465 470
Jacobian 156 657
Jahnke 524 568
Jump function 221
Kadyrov, M. 674
Kagan, B.M. 114 676
Kantorovich theorem 465
Kantorovich, L.V. 161 228 465 481 506 676
Kantorovich, method of (for isolating singularities) 635
Khaletsky, scheme of 295 297
Khinchin, A.Ya. 76 676
Khovanskv, A.N. 76 114 676
Kimball, G.E. 674 677
Kitov, A.I. 674 676
Krinitsky, N.A. 674 676
Kronecker delta 230
Krylov, A.N. 54 189 202 217 228 589 648 676
Krylov, method of 217 225 411 421ff
Krylov, method of, computation of eigenvectors by 424
Krylov, V.I. 225 648 676
Kummer transformation 203 204
Kurosh, A.G. 202 409 458 676
Lagrange's interpolation formula 539 541
Lagrange's theorem 168
Lagrange, method of 169
Lagrangian coefficients 543
Lagrangian coefficients, computational scheme for 546 547
Lagrangian coefficients, computing 543
Lambda-difference 440
Lambert's formula 100
latent root 375
Law chain 668
Law, propagation (of  -error) 515
Lednev, N.A. 573 676
Legendre polynomials 611
Leibniz, Newton — Leibniz formula 590
Length of a vector 345
Leverrier, method of 411
Limiting absolute error 20ff
Limiting relative error 21
Limiting relative error, tables for determining 30
Lin's method 201
Linear dependence of vectors 337
Linear equations, solving systems of 273ff
Linear subspace 341
Linear subspace, invariance of 379
Linear system, normal 312
Linear system, reducing (to a form convenient for iteration) 307
Linear transformations of variables 367
Linear transformations, degenerate 374
Linear transformations, operations with 371
Linear transformations, singular 374
Linear vector spaces 336ff
Linear vector spaces, theory of 336ff
Linear-transformation operator 369
Linearly dependent vectors 337
Linearly independent vectors 337
Lines (of a matrix) 229
Lobachevsky — Graeffe method 179 182
Lobachevsky — Graeffe method for case of complex roots 187 192
Lobachevsky — Graeffe method for case of real and distinct roots 184
Lobachevsky, N.I. 182
Logarithmic function 95
Logarithms 49
Loss of accuracy in subtraction 35
Lyapin, E.S. 272 676
Lyusternik, L.A. 114 453 458 676
Lyusternik, method of 453ff
Maclaurin's series 89
Maclaurin, Euler — Maclaurin formula 628 630
Major approximation 19
Maltsev, A.I. 272 393 676
Mapping, contraction 487ff
Markov chain, discrete 667
Markov's formula 566
Markov, A. 114 228 648 676
Matrices see "Matrix"
Matrix (matrices) of quadratic form 311
Matrix (matrices), absolute value of 242
Matrix (matrices), adjoint of 236
Matrix (matrices), bilinear expansion of 392
Matrix (matrices), bilinear form of 384
Matrix (matrices), bordered 257
Matrix (matrices), change-of-basis 348
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