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| Demidovich B.P., Maron I.A. — Computational Mathematics |
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| Предметный указатель |
Remainder term of Stirling's interpolation formula 552
Remainder term, Simpson's formula and its 596
Remainder term, trapezoidal formula and its 595
Remez, E.Ya. 573 677
Residual 285
residual error 23
Reverse procedure 280 see
Richardson extrapolation 622ff
Richardson, method of 320
Robinson, G. 161 272 573 678
Rolle's theorem 133
Root squaring 182
Root(s) of a system of equations 274
Root(s) of an equation 115
Root(s), characteristic 375
Root(s), complex 190 see
Root(s), existence of (of a system) 469
Root(s), finding (by inverse interpolation) 564
Root(s), improving 284
Root(s), isolation of 115
Root(s), latent 375
Root(s), multiplicity of 162
Root(s), real (bounds of) 167
Root(s), real (of a polynomial) 173
Root(s), relative error of 41
Root(s), separated 180
Root(s)-fold (s-fold) 178
Root-squaring process 182
Rotation transformation 370
Rounding errors 29
Rounding of numbers 26ff
Rounding-off rule 26
Row vector 229
Rule of signs, Descartes' 178
Rule, Cramer's 273
Rule, even-digit 26
Rule, parabolic 603
Rule, rounding-off 26
Rule, Simpson's 597
Rule, three eighths 599
Rule, trapezoidal 601
Runge, C. 589 677
Salekhov, G. 228 677
Salvadori, M.G. 321 648 677
Sampling error 666
scalar 229
Scalar product(s) of vectors 343
Scalar product(s) of vectors, properties of 343
Scalar product(s), method of 436
Scarborough, J.B. 54 161 321 506 573 589 648 677
Scheme of Knaletsky 295 297
Scheme of unique division 280
Scheme, Horner's 77 78
Scheme, Horner's, generalized 80—81
Schreier, O. 272 677
Scientific notation 18 24
Secular determinant(s) 376 565
Secular determinant(s), expansion of 410ff
Secular determinant(s), expansion of, comparison of different methods of 429
Secular equation 376
Seidel method 309ff
Seidel process 155
Seidel process, convergence of 327 330 333
Seidel process, estimating the error of approximations in 330
Seidel process, estimating the error of approximations in, by l-norm 332
Seidel process, estimating the error of approximations in, by m-norm 330
Separated roots 180
Sequence, convergent (of matrices) 249
Sequence, Gaussian random 652
Sequence, pseudorandom 654
Sequence, random 651
Sequence, Sturm 174
Series, convergence of, acceleration of 89
Series, Fourier trigonometric 213
Series, Madaurin's 89
Series, matrix, sum of 251
Series, numerical 83
Series, numerical, convergent 83
Series, power 504 see
Series, sum of 83
Series, Taylor's 89
Shabat, B.V. 202 675
Shapiro, G.M. 202 677
Shestakov, V.I. 114 676
Shilov, G.E.A. 393 677
Shreider, Yu.A. 393 674 677
Shura-Bura, M.R. 114 676
SIGN 86
Sign changes 174
Sign(s), Descartes' rule of 178
Sign(s), variations of 174 see
Significant digit 24
Signum function 86
Similar matrices 339 380
Similar matrices, symbol for 339 380
Simple continued fraction 56
Simpson type cubature formula 644
Simpson's cubature formula 645
Simpson's formula and its remainder term 596
Simpson's general formula 603
Simpson's rule, formula of 597
Singular linear transformation 374
Singular matrix 236
Singular transformation 375
Singularities, isolation of by Kantorovich method 635
Smirnov, V.I. 114 409 677
Smolitsky, Kh.L. 321 677
Solution set (of a system of equations) 274
Solution space of a homogeneous system 364f
Solution(s) of a difference equation 198
Solution(s), approximate (of systems of nonlinear equations) 459
Solution(s), fundamental system of 365
Solution(s), graphical 119
Space, basis of 340
Space, generated by vectors 342
Space, linear vector 336ff
Space, n-dimensional 336
Space, n-dimensional real 344
Space, n-dimensional, point of 336
Space, n-dimensional, vector of 336
Space, solutions 364
Space, spanned by vectors 342
SPACING 507 see
Span (spanned by vectors) 342
Sperner, E. 272 677
Square matrix 229
Square roots, computing 107
Square-root method 293
Standard continued fraction 56
Steepest descent, method of 496 499
Steepest descent, method of, for a system of linear equations 501
| Steffensen, J.F. 599 648 677
Stenin 465
Stirling's expansion 207
Stirling's interpolation formula 533
Stirling, J. 205
Sturm method 173
Sturm sequence 174
Sturm's theorem 174
Submatrix (submatrices) 256
Subspace, dimensionality of 342
Subspace, linear 341
Substitution, back 280
Substitution, forward 280
Subtraction, loss of accuracy jn 35
Sum(s) of a series 83
Sum(s), check 281
Sum(s), error of 33
Sylvester conditions 389
Symmetric matrix (matrices) 235 384
Symmetric matrix (matrices), properties of 384
Symmetry, Hermitjan 343
System(s) of linear algebraic equations, solution of by Monte Carlo method 666
System(s) of linear equations, solution of by orthogonalization methods 358
System(s) of linear equations, solving 273ff
System(s) of nonlinear equations, approximate solution of 459ff
System(s), fundamental (of solutions) 365
System(s), normal 311
System(s), normal linear 312
System(s), orthogonal 345
Table(s) for determining limiting relative error 30
Table(s) of central differences 530
Table(s) of divided differences 556
Table(s) of random numbers 653
Table(s) of random numbers, compilation of 653 654 656
Table(s), Barlow's 113
Table(s), difference 510 see
Table(s), double-entry 569
Tangents, method of 127
Taylor polynomial 89
Taylor's series 89
Taylor's series, remainder 89
Taylor's series, term of kth component of continued fraction 55
Ter-Mikaelyan, T.M. 114 676
Test, Cauchy's 83
Theorem of Budan — Fourier 175 176
Theorem of Pringsheim 71
Theorem, Cayley — Hamilton 397
Theorem, convergence 214
Theorem, fundamental (of algebra) 162
Theorem, Hua's 179
Theorem, Hurwitz 406
Theorem, Kantorovich 465
Theorem, Lagrange's 168
Theorem, Newton's 171
Theorem, Ostrowski's 159 465
Theorem, Perron's 390
Theorem, Rolle's 133
Theorem, Sturm's 174
Theorem, Weierstrass 389
Theory of continued fractions 55ff
Theory of errors 42
Theory of errors, inverse problem of 44
Theory of errors, inverse problem of, second 48
Three-eighths rule 599
Tolstoy, G.P. 114 161 228 677
Trace of a matrix 377
Trajectory 668
Transformation matrix 368
Transformation(s) 367
Transformation(s) by a matrix, properties of 381
Transformation(s) of coordinates of a vector under changes in the basis 348
Transformation(s), Euler — Abel 210
Transformation(s), identical 375
Transformation(s), inverse 373
Transformation(s), Kummer 203 204
Transformation(s), linear (of variables) 367
Transformation(s), linear (of variables), degenerate 374
Transformation(s), linear (of variables), operating with 371
Transformation(s), linear (of variables), singular 374
Transformation(s), nonsingular 374
Transformation(s), projection 369
Transformation(s), rotation 370
Transformation(s), singular 375
Transition probabilities 667
Transition probability matrix 667—668
Transpose of a matrix 234
Transpose of a matrix, properties of 235
Trapezoidal formula and its remainder term 595
Trapezoidal rule 601
Triangular matrices 265
Trigonometric approximation 225
Trigonometric functions 49 98
Trigonometric functions, computing values of 98
Undetermined coefficients, method of 411
Unique division, scheme of 280
Unit matrix 230
Vandermonde determinant 592 614
Variable interval 555
Variations of sign 174
Variations of sign, lower number of 175
Variations of sign, upper number of 176
Vector(s) of n-dimensional space 336
Vector(s), angle between two 345
Vector(s), column 229
Vector(s), coordinates of 336 341
Vector(s), length of 345
Vector(s), linear dependence of 337
Vector(s), linearly dependent 337
Vector(s), linearly independent 337
Vector(s), negative of 336
Vector(s), orthogonal 345
Vector(s), orthogonal systems of 345
Vector(s), product of 337
Vector(s), product of by a scalar 337
Vector(s), row 229
Vector(s), scalar product of 343
Vector(s), scalar product of, properties of 343
Vector(s), zero 336
Ventsel, D.A. 54 161 677
Ventsel, E.S. 54 161 506 674 677
Very much less than ( ) 22
Volume, algebraic 656
Wayland, Harold 458 678
Weierstrass theorem 389
Whittaker, E.T. 161 272 573 678
Willers, F.A. 465
Young's modulus 44
Zaguskin, V.L. 202 678
Zero matrix 230
Zero of a function 115
Zero vector 336
Zhidkov, N.P. 321 458 648 675
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