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| Demidovich B.P., Maron I.A. — Computational Mathematics |
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| Предметный указатель |
Abel, Euler — Abel transformation 210
Abel, N.H., Euler — Abel method 209
Abramov, A.A. 114 676
Absolute error 19
Absolute value of a matrix 242
Absorbing barrier 667
Acceleration of convergence of Fourier trigonometric series by Krylov's method 217
Acceleration of convergence of numerical series 203
Acceleration of convergence of power series by Euler — Abel method 209
Acceleration of convergence of series 89
Accumulation, method of 306 640
Accuracy in determination of arguments from a tabulated function 48
Accuracy of quadrature formulas 618
Accuracy, estimation of 17
Additive inverse of a matrix 232
Adjoint of a matrix 236
Algebra, fundamental theorem of 162
Algebra, matrix 229
Algebraic equations, approximate solution of (special techniques for) 162ff
Algebraic equations, bounds of real roots of 167
Algebraic equations, general properties of 162ff
Algebraic volume 656
Algorithm, Euclid's 165
Algorithm, Hero's 107
Alternating sums, method of 169
Analysis, classical 5
Analytic functions, computing values of 89
Angle between two vectors 345
Approximate differentiation 574ff
Approximate differentiation, formulas of, based on Newton's first interpolation formula 575
Approximate differentiation, formulas of, based on Stirling's formula 580
Approximate integration 590ff
Approximate numbers 19ff
Approximate solution of algebraic equations, special techniques for 162ff
Approximation of improper integrals 633
Approximation, major 19
Approximation, minor 19
Approximation, trigonometric 225
Argument, principle of 166
Back substitution 280 see
Backward extrapolation 529
Backward interpolation 529
Barlow's tables 113
Baron, M.L. 321 648 677
Barrier, absorbing 667
Bases see "Basis"
Basis (bases) of a space 340
Basis (bases) of a space, initial 341
Basis (bases), biorthogonal 391
Basis (bases), normalized orthogonal 346
Basis (bases), orthogonal 346
Basis (bases), orthonormal 346
Beckenbach, E.F. 321 506 674 675
Berezin, I.S. 321 458 645 675
Bernoulli method 198ff
Bernoulli numbers 99 208 625ff
Bernoulli numbers, generating function of 627
Bernstein, S.N. 608
Bessel's formula for parabolic interpolation 535
Bessel's function of order zero 582
Bessel's inequality 216
Bessel's interpolation formula 534 535
Bezikovich, Ya.S. 54 161 228 675
Bilinear expansion of a matrix 392
Bilinear form of a matrix 384
Biorthogonal bases 391
Biorthogonality relations 390 393
Biorthogonality, conditions of 390
Blocks of a matrix 256
Bordered matrices 257
Bordering, method of (matrices) 262
Bounds of real roots of algebraic equations 167
Bounds, method of 50
Bradis, V.M. 54 573 675
Brown, G.W. 674
Budan, theorem of Budan — Fourier 175 176
Bulgakov, B.V. 272 675
But, E. 506 675
Canonical convergents 59
Canonical norm of a matrix 243
Cardan's formula 186
Cauchy inequality 245
Cauchy test 83
Cayley — Hamilton theorem 397
Central derivatives, formulas for 580
Central differences 530
Central formulas 580
Central-difference formulas 531
Chain law 668
Chain, discrete Markov 667
Change-of-basis matrix 348
Characteristic determinant 376 565
Characteristic equation 376
Characteristic matrix 376
Characteristic number 375 377
Characteristic polynomial 376 382
Characteristic root 375
Chebyshev polynomial 554
Chebyshev's quadrature formula 607ff
Chebyshev, P.L. 554
Check sums 281
Check, final 17
Check, intermediate 17
Chords, method of 122
Class, periodicity 214
Classical analysis 5
Coefficients, Cotes 594 600
Coefficients, Fourier 213
Coefficients, Lagrangian 543
Collar, A.R. 272 675
Column vector 229
Combination method 136
Commutative matrices 234
Complex roots, one pair of 190
Complex roots, two pairs of 194 197
Components of continued fractions, terms of 55
Computation sheets 16
Computation work, rules of 15ff
Computation(s) see also "Computing"
Computation(s) in which errors are not taken into exact account 42
Computation(s) of determinants 269
Computation(s), double, method of 50
Computational scheme of Danilevsky's method 416
Computing see also "Computation"
Computing, analytic functions 89
Computing, cube roots 112
Computing, exponential functions 91
Computing, forms 16
Computing, functions 77ff
Computing, hyperbolic functions 101
Computing, logarithmic functions 95
Computing, polynomials 77
Computing, rational fractions 82
Computing, reciprocals 104
Computing, reciprocals of square roots 111
Computing, square roots 107
Computing, trigonometric functions 98
Conditions of biorthogonality 390
Conditions, Hurwitz 406
Conditions, Sylvester 389
Conformal partitioned matrices 257
Continued fraction(s) 55
Continued fraction(s), components of 55
Continued fraction(s), conversion of to a simple fraction 56
Continued fraction(s), expanding functions into 72ff
Continued fraction(s), infinite 55
Continued fraction(s), n-component 55
Continued fraction(s), nonterminating 66
Continued fraction(s), nonterminating, convergent 66
Continued fraction(s), nonterminating, divergent 67
| Continued fraction(s), simple 56
Continued fraction(s), standard 56
Continued fraction(s), theory of 55f
Contraction mapping 487ff
Convergence of Fourier trigonometric series (acceleration of by Krylov method) 217
Convergence of iteration processes for systems of linear equations 322ff 394ff
Convergence of iteration processes for systems of linear equations, necessary and sufficient conditions for 398
Convergence of iteration processes for systems of linear equations, sufficient conditions for 322
Convergence of iteration processes, first sufficient condition of 491
Convergence of iteration processes, second sufficient condition of 493
Convergence of matrix power series 394
Convergence of numerical series, accelerating 203
Convergence of power series, acceleration of by Euler — Abel method 209
Convergence of Seidel process for a normal system 403
Convergence of Seidel process, first-sufficient condition for 327
Convergence of Seidel process, necessary and sufficient conditions for 400
Convergence of Seidel process, second sufficient condition for 330
Convergence of Seidel process, third sufficient condition for 333
Convergence of series, acceleration of 89
Convergence of the Newton process 465 469
Convergence of the Newton process, rapidity of 474
Convergence of the Newton process, stability of 478
Convergence theorem 214
Convergence, accelerating (by Lyusternik method) 453 458
Convergence, methods for effectively checking the conditions of 405
Convergent integral 633 635
Convergents 58ff
Convergents, canonical 59
Convergents, law of formation of 59
Coordinates of a vector 336
Coordinates of a vector in a basis 341
Correct digit 25
Cotes coefficients 594 600
Cotes, Newton — Cotes formulas 599
Cotes, Newton — Cotes quadrature formulas 593
Cramer's formulas 276
Cramer's rule 273
Cubafure formulas 590 641ff
Cubafure formulas of Simpson type 644
Cubafure formulas, Simpson's 644
Cubature, mechanical 590
Cube roots, computation of 112
Danilevsky, A.M., method of 412
Danilevsky, computational scheme of 416
Danilevsky, exceptional cases in 418
Danilevsky, method of, computation of eigenvector's by 420
Davis, P. 674 675
De La Vallee-Poussin, C.J. 228 677
Degenerate linear transformation 374
DEL 497
Delta, Kronecker 230
Delta, the operator  508
Derivatives, central 580
Derivatives, partial 588
Descartes' Rule of Signs 178
Descent, steepest 496 499 see
Determinant(s) 230
Determinant(s), characteristic 376 565
Determinant(s), computation of 269
Determinant(s), Gaussian method in computing 288
Determinant(s), secular 376 565
Determinant(s), secular, expansion of 410ff 429
Determinant(s), Vandermonde 592 614
Diagonal difference table 511
Diagonal matrix 229 265
Difference equation 198
Difference table 510
Difference table, diagonal 511
Difference table, horizontal 511
Difference(s), central 530
Difference(s), divided 554ff
Difference(s), double (of higher order) 570
Difference(s), error of 34
Difference(s), finite 507ff
Difference(s), lambda ( -difference) 440
Differentiation operator 629
Differentiation, approximate 574ff
Differentiation, graphical 586
Differentiation, Numerical 583
Digit, correct 25
Digit, significant 24
Dimensionality of a subspace 342
Direct procedure 280 see
Discrete Markov chain 667
Distribution function 651
Distributivity 344
Divergent integral 633 635
Divided differences 554ff
Divided differences, table of 556
Double computation, method of 50 622
Double differences of higher order 570
Double-entry table 569
Duncan, W.J. 272 675
Eigenvalue(s) 375 377 382 445
Eigenvalue(s), extremal property of 387
Eigenvalue(s), finding (of a matrix) 410ff
Eigenvalue(s), finding the first 436
Eigenvalue(s), finding the numerically largest 430
Eigenvalue(s), finding the second 439
Eigenvector(s) 375 382 445ff
Eigenvector(s), computation of by Danilevsky's method 420
Eigenvector(s), computation of by Krylov's method 424
Eigenvector(s), finding 410ff 430 439 see
Element(s) of a matrix 229
Element(s), principal 287
Emde 524 568
Empirical formula 524
Entries (of a matrix) 229
Equal effects, principle of 45
Equation(s), algebraic 162
Equation(s), characteristic 376
Equation(s), difference 198
Equation(s), equivalent 119
Equation(s), graphical solution of 119
Equation(s), linear 273
Equation(s), nonlinear 459 see
Equation(s), root of 115ff
Equation(s), secular 376
Equation(s), solution of 199
Equivalent equations 119
Equivalent matrices 268
Error estimate, probability 52
Error(s) 19
Error(s) of a difference 35
Error(s) of a product 37
Error(s) of a quotient 40
Error(s) of a sum 33
Error(s) of method 22 621
Error(s) of operation 23 84
Error(s) of the problem 22
Error(s), absolute 19
Error(s), computations in which errors are not taken into exact account 42
Error(s), epsilon ( -error) (propagation law of) 515
Error(s), general formula for 42
Error(s), initial 23
Error(s), limiting absolute 20
Error(s), limiting relative 21
Error(s), relative 19 21 see
Error(s), residual 23
Error(s), rounding 23
Error(s), sampling 666
Error(s), sources of 22ff
Error(s), theory of 42
Escalator method 320
Euclid's Algorithm 165
Euler — Abel method 209
Euler — Abel transformation 210
Euler — Maclaurin formula 628 630
Euler — Maclaurin summation formula 630
Euler, L. 58
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