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| Demidovich B.P., Maron I.A. — Computational Mathematics |
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| Предметный указатель |
Matrix (matrices), characteristic 376
Matrix (matrices), commutative 234
Matrix (matrices), conformal partitioned 257
Matrix (matrices), diagonal 229 265
Matrix (matrices), difference of 231
Matrix (matrices), eigenvalues of 375
Matrix (matrices), eigenvectors of 375
Matrix (matrices), elementary transformations of 268
Matrix (matrices), equality of 230
Matrix (matrices), equivalent 268
Matrix (matrices), Frobenius 412 415 418
Matrix (matrices), inverse 236 239
Matrix (matrices), inversion of 273 see
Matrix (matrices), Jacobi 465 470
Matrix (matrices), limit of 249
Matrix (matrices), minor of 248
Matrix (matrices), modulus of 242
Matrix (matrices), multiplication of 232
Matrix (matrices), multiplication of, by a scalar 231
Matrix (matrices), nonsingular 236
Matrix (matrices), norm of 242 243
Matrix (matrices), nullity of 248
Matrix (matrices), operations involving 230
Matrix (matrices), orthogonal 350
Matrix (matrices), orthogonal, method of 363
Matrix (matrices), orthogonal, properties of 350
Matrix (matrices), orthogonalization of 351
Matrix (matrices), positive definite symmetric real 388
Matrix (matrices), powers of 240
Matrix (matrices), product of 231
Matrix (matrices), quasidiagonal 256
Matrix (matrices), rank of 248
Matrix (matrices), rational functions of 241
Matrix (matrices), real 389
Matrix (Matrices), rectangular 229
Matrix (matrices), series of 251 see
Matrix (matrices), similar 339 380
Matrix (matrices), singular 236
Matrix (Matrices), square 229
Matrix (matrices), sum of 231
Matrix (matrices), symmetric 235 384
Matrix (matrices), trace of 377
Matrix (matrices), transformation 368
Matrix (matrices), transition probability 667
Matrix (matrices), transpose of 234
Matrix (matrices), triangular 265
Matrix (Matrices), unit 230
Matrix (matrices), zero 230
Matrix algebra 229
Matrix inversion 236
Matrix inversion by partitioning 260
Matrix inversion, using the coefficients of the characteristic polynomial of a matrix for 450
Matrix power series, convergence of 394
Matrix series, absolutely convergent 252
Mechanical cubature 590
Mechanical quadrature 590
Mesh points 518
Method(s) for effectively checking the conditions of convergence 405
Method(s) modified Newton 135
Method(s) of A.A. Abramov 458
Method(s) of A.M. Danilevsky 412
Method(s) of A.M. Danilevsky, computation of eigenvectors by 420
Method(s) of A.M. Danilevsky, computational scheme of 416
Method(s) of A.M. Danilevsky, exceptional cases in 418
Method(s) of A.N. Krylov 217 225 411 421ff
Method(s) of A.N. Krylov, computation of eigenvectors by 424
Method(s) of accumulation 306 640
Method(s) of alternating sums 169
Method(s) of bordering (matrices) 262
Method(s) of bounds 50
Method(s) of chords 122
Method(s) of double computation 50 622
Method(s) of exhaustion 443 444
Method(s) of iteration 138ff 300 302 484ff
Method(s) of L.A. Lyusternik 453ff
Method(s) of L.V. Kantorovich (for isolating singularities) 635
Method(s) of Lagrange 169
Method(s) of Leverrier 411 426
Method(s) of Lobachevsky — Graeffe 179 182
Method(s) of M.K. Gavurin 458
Method(s) of N.V. Paluver 201
Method(s) of orthogonal matrices 363
Method(s) of power series 504
Method(s) of principal elements 287
Method(s) of proportional parts 122
Method(s) of Purcell 320
Method(s) of relaxation 313ff
Method(s) of Richardson 320
Method(s) of scalar products (for finding first eigenvalue of a real matrix) 436
Method(s) of steepest descent 496 499
Method(s) of steepest descent for a system of linear equations 501
Method(s) of successive approximations 138
Method(s) of tangents 127
Method(s) of undetermined coefficients 411 428ff
Method(s), Bernoulli's 198ff
Method(s), combination 136
Method(s), escalator 320
Method(s), Euler — Abel 209
Method(s), exact (in solving systems of linear equations) 273
Method(s), Gaussian 277ff see
Method(s), gradient 496
Method(s), halving 121
Method(s), interpolation 411
Method(s), iterative (in solving systems of linear equations) 273
Method(s), Lin's 201
Method(s), Monte Carlo 649ff
Method(s), Newton 127 171 459f
Method(s), Newton, modified 481ff
Method(s), nomographic 121
Method(s), Seidel 309ff
Method(s), square-root 293
Method(s), Sturm 173
Mikeladze, Sh.E. 589 648 676
Milne, W.E. 458 506 573 589 648 674 677
Minor (of a matrix) 248
Minor approximation 19
Mlodzeyevsky, B.K. 202 677
Modified Newton method 135
Modulus 242
Modulus of a matrix 242
Modulus, Young's 44
Monte Carlo evaluation of multiple integrals 656
Monte Carlo method 649ff
Monte Carlo method, problems attacked by 650
Monte Carlo method, solving systems of linear algebraic equations by 666
Morrey, C.B., Jr. 506
Morse, P.M. 674 677
Multiple integrals, Monte Carlo evaluation of 656
Multiplicity of a root 162
nabla 497
Negative definite quadratic form 312
Negative of a matrix 232
Negative of a vector 336
Newton — Cotes formulas of higher orders 599
Newton — Cotes quadrature formulas 593
Newton — Leibniz formula 590
Newton's first interpolation formula 522 526
Newton's interpolation polynomial 521
Newton's method 127 171 459ff
Newton's method for a system of two equations 156
Newton's method for complex roots 157
Newton's method, modified 35 481ff
Newton's process, convergence of 465 469
Newton's process, convergence of, rapidity of 474
Newton's process, convergence of, stability of 478
Newton's quadrature formula 599
Newton's second interpolation formula 526 527
Newton's Theorem 171
Nikolsky, S.M. 592 648 677
Nomographic methods 121
| Nonlinear equations 459 see
Nonsingular matrix 236
Nonsingular transformation 374
Nonterminating continued fractions 66
Nonterminating continued fractions, convergent 67
Nonterminating continued fractions, divergent 67
Norm of a matrix 242 243
Norm of a matrix, canonical 243
Norm of a matrix, k-norm, l-norm, m-norm 243
Normal linear system 312
Normal system 311
Normalized orthogonal basis 346
Notation, powers-of-ten 18 24
Notation, scientific 18 24
Nullity of a matrix 248
Number(s), approximate 19ff
Number(s), Bernoulli 99 208 625ff
Number(s), characteristic 375 377
Number(s), exact 19
Number(s), pseudorandom 653
Number(s), random 650 see
Numerical differentiation, formulas for equally spaced points 583
Numerical series 83
Numerical series, approximation of sums of 83
Numerical series, convergent 83
Operator, differentiation 629
Operator, finite-difference 628
Operator, linear-transformation 369
Orthogonal basis 346
orthogonal matrices 350
Orthogonal matrices, method of 363
Orthogonal matrices, properties of 350
Orthogonal systems of vectors 345
Orthogonal vectors 345
Orthogonality 345
Orthogonalization methods, application of to solution of systems of linear equations 358
Orthogonalization of columns 358
Orthogonalization of matrices 351
Orthogonalization of rows 361
Orthonormal basis 346
Ostrowski's theorem 159 465
Ostrowski, A. 465 506 677
Paluver, method of 201
Paluver, N.V. 201
Parabolic interpolation 522
Parabolic rule 603
Partial derivatives, approximate calculation of 588
Partial quotients 56
Partitioned matrix (matrices) 256
Partitioned matrix (matrices), addition of 257
Partitioned matrix (matrices), conformal 257
Partitioned matrix (matrices), multiplication of 258
Partitioned matrix (matrices), subtraction of 257
Partitioning, matrix inversion by 260
Path 668
Periodicity class 214
Perpendicularity 345
Perron's theorem 390
Perron, O. 76 677
Point(s) of n-dimensional space 336
Point(s), interpolation 518 see
Point(s), mesh 518
Polynomial(s), characteristic 376 382
Polynomial(s), Chebyshev 554
Polynomial(s), computing values of 77
Polynomial(s), left 241
Polynomial(s), Legendre 611
Polynomial(s), real roots of (number of) 173
Polynomial(s), right 241
Polynomial(s), Taylor 89
Positive definite quadratic form 312
Positive definite symmetric real matrix 388
Positive definiteness, property of 343
Postmultiplication 236
Postmultiplier 269
Power series, accelerating convergence of (by Euler — Abel method) 209
Power series, method of 504
Power, generalized 517
Power, relative error of 41
Powers-of-ten notation 18 24
Preinultiplier 269
Premultiplication 236
Principal element(s) 267
Principal element(s), method of 287
Principal row 287
Principle of equal effects 45
Principle of the argument 166
Pringsheim theorem 71
Probabilities, transition 667
Probability error estimate 52
Probability integral 561
Problem of interpolation (statement of) 518
Procedure, direct and reverse 280
Process, Hero's 107
Process, Newton 465
Process, root-squaring 182
Process, Seidel 155
Product of matrices 231
Product, error of 37
Product, number of correct digits in a 39
Product, scalar (of vectors) 343
Product, scalar (of vectors), properties of 343
Projection transformation 369
Propagation law of the  -error 515
Proper integral 633
Properties of 611
Proportional parts, method of 122
Pseudorandom numbers 653
Pseudorandom sequence 654
Purcell, method of 320
Quadratic form 311
Quadratic form, matrix of 311
Quadratic form, negative definite 312
Quadratic form, positive definite 312
Quadrature formulas 590
Quadrature formulas of closed type 591
Quadrature formulas of open type 591
Quadrature formulas, accuracy of 618
Quadrature formulas, Chebyshev's 607ff
Quadrature formulas, Gauss' 611 614
Quadrature formulas, Newton — Cotes 593
Quadrature formulas, Newton's 599
Quadrature, mechanical 590
Quantity, random 651
Quasidiagonal matrices 256
Quotient(s), error of 41
Quotient(s), number of correct digits in a 41
Quotient(s), partial 56
Rabinowitz, P. 674 675
Random numbers 650
Random numbers, generating 653
Random numbers, tables of 653
Random quantity 651
Random sequence 651
Random sequence, Gaussian 652
Randomizing devices 653
Rank of a matrix 248
Rational fractions, computing values of 82
Real matrices 389
Reciprocals of square roots, computing 111
Reciprocals, computing 104
Rectangular matrix 229
Relations, biorthogonality 390 393
Relative error 19 21
Relative error of a power 41
Relative error of a root 41
Relative error of approximate number and number of correct digits 27ff
Relaxation, method of 313ff
Remainder term 89
Remainder term of Bessel's interpolation formula 552
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