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| Ralston A., Wilf H.S. — Mathematical methods for digital computers |
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| Предметный указатель |
Acceleration parameters 228
ALCOR 8
Algol 1
ALGOL, array declarations 10
ALGOL, basic symbols 8
ALGOL, block structure 25—28
ALGOL, constants and variables 9
ALGOL, control statements 13—17
ALGOL, expressions 11
ALGOL, input-output 21
ALGOL, limitations of 31
ALGOL, logical expressions 12
ALGOL, programming 5 et seq.
ALGOL, sample program 22
ALGOL, subroutines 17—21
ALGOL, switch declaration 28
ALGOL, syntactical definitions 23—25
Alternating direction methods 215 et seq.
Approximate integration formulas 145
Asymptotic efficiency 190
Asymptotic error constant 173
Asymptotic expansions 55
Asymptotic expansions, converging factors of 56
Back substitution 73
Back substitution, error analysis of 81—82
Bairstow’s method 50 192
Bernoulli method 198
Bubble sort 5
Cartesian product formula 146
Chebyshev approximation 264 et seq.
Cholesky factorization 71 94
Companion matrix 54
Computational efficiency 181—182
Condition number 74
Condition number, spectral 74
Condition of a polynomial 186
Condition of a polynomial, deterioration of 194
Consistent matrix norm 66
Continued fraction 56
Correlation variates 255—256
Courant — Fischer theorem 100
Crout decomposition 71 73 80
Defect 266
Deflation 123 188
Degenerate approximation 266
Degree 145
Designational imperative 6
Difference scheme 37
Dimension statement 10
Divided differences 159 161
Doolittle’s method 71 73 80
Doolittle’s method, error analysis 78
Double FG algorithm 119
Double QR transformation 120 122
Dummy statement 16
Eigenvalue bounds 225
Eigenvalues of symmetric matrices 94 et seq.
Eigenvalues of tridiagonal matrix 96—98
Elementary hermitian matrix 66
Elementary matrix 66
Equilibration 80
Essential convergence 117
Euclid’s algorithm 194
Euler — Maclaurin formula 135
Exchange algorithm 266
Exponential distribution 255
Extended QD scheme 41
Factorization of a matrix 69
FG algorithm 117
FG algorithm, double 119
Fibonacci sequence 251
Formal Laurent series 39
format strings 22
FORTRAN 1 2
FORTRAN, aray declarations 10
FORTRAN, basic symbols 8
FORTRAN, constants and variables 8
FORTRAN, control statements 13—17
FORTRAN, expressions 10
FORTRAN, input-output 21
FORTRAN, limitations of 31
FORTRAN, logical expressions 12
FORTRAN, programming 5 et seq.
FORTRAN, sample program 22
FORTRAN, subroutines 17—21
Forward substitution 73
Forward substitution, error analysis of 81—82
Frobenius norm 67
Gauss quadrature 137
Gauss quadrature, Legendre quadrature 146
Gauss quadrature, Tschebycheff quadrature 137
Gaussian 251
Gaussian elimination 67ff 99
Gaussian elimination error analysis 76
Gaussian elimination with complete pivoting 68
Gaussian elimination with partial pivoting 68
Gerschgorin’s lemma 54
Givens — Householder method 94ff
Givens — Householder method, error analysis 100
Graeffe procedure 54 192
Gram — Schmidt process 117
Green’s Theorem 219
Hailey’s iteration 174
Hankel determinants 38
Heat conduction 215 et seq.
Heat conduction, time dependent 233
Hessenberg form 119
Horner’s method 54
HOT 1 236
Ill-conditioned equations 65 et seq.
Ill-conditioned equations, error analysis 73
Ill-conditioned polynomials 186
Interpolation theory 175
Interpolation theory, inverse 175
Interpolation theory, Lagrangian 156 175
Interpolation theory, Newtonian 175
Inverse interpolation 175
Iteration function 172
Iteration function with memory 174
Iteration function, choice of 182
Iteration function, examples of 178
Iteration function, multipoint 172 178
Iteration function, one point 173 et seq.
Iteration function, order of 173
Jacobian matrix 181
Jacobi’s method 94
Jensen’s Inequality 138
Lagrangian interpolation 156 175
Laguerre’s method 189
Lehmer — Schur method 191
| Lower triangular matrix 69
LR algorithm (see LU algorithm)
LU algorithm 116 et seq.
LU algorithm, convergence of 117
LU algorithm, origin shifts in 118—119
LU algorithm, stability of 122
Matrix, Cholesky factorization of 71
Matrix, condition number of 74
Matrix, consistent 66
Matrix, Crout decomposition of 71
Matrix, elementary 66
Matrix, elementary Hermitian 66
Matrix, Hessenberg 119
Matrix, norms 66 95
Matrix, orthogonal triangularization of 72
Matrix, triangular factorization of 69
Matrix, tridiagonal 95
Mid-square method 250
Monte Carlo 250
Monte Carlo, quadrature 139
Muller’s method 190
Multiple quadrature 145 et seq.
Multiple zeros 180
Multiplicative congruential procedure 251
Multipoint iteration function 172
Newton — Raphson method 172 189
Newtonian interpolation 175
Newton’s identities 138
Nonlinear equations 171 et seq.
Nonuniform distributions 254
Normal distribution 255
One point iteration functions 172—174
One point iteration functions, fundamental theorem of 177—178
One-for-one exchange algorithm 266
Order of a sequence 173
Order of an iteration function 173
Orthogonal triangularization 72
Pade approximations 234
Parabolic equation 216
Peaceman — Rachford method 223
Peano’s theorem 159
Peano’s theorem, kernel 159
Perturbation theory 73
Perturbed QD scheme 38
Pivoting 67
Pivoting, complete 68
Pivoting, growth factor with 81
Pivoting, necessity for 79
Pivoting, partial 68
Polynomial, condition of 186
Polynomial, deflation of 188
Polynomial, equations 185 et seq.
Polynomial, evaluation of 187
Power method 99
Product formulas 146
Pseudorandom sequence 249
Pseudorandom sequence, period of 251
Pseudorandom sequence, serial correlation of 253
Pseudorandom sequence, testing of 254
qd algorithm 37 et seq.
QR algorithm 116 et seq.
QR algorithm, convergence of 117
QR algorithm, double 120 122
QR algorithm, stability of 122
Quadrature 133 et seq.
Quadrature and analytic functions 140
Quadrature, Gauss — Legendre 146
Quadrature, Gaussian 137
Quadrature, Monte Carlo 139
Quadrature, multiple 145 et seq.
Quadrature, Newton — Cotes 137
Quadrature, over a sphere 148
Quadrature, Romberg 133
Quadrature, Tschebycheff 137—139
Quotient-difference scheme 38
Quotient-difference scheme, extended 41—42
Quotient-difference scheme, perturbed 38—41
random number generation 249 et seq.
Random number generation, congruential 251
Random number generation, midsquare 250
Randomness, tests of 254
Rational arithmetic 61
Rational Chebyshev approximation 264 et seq.
Rayleigh quotient 102
Recursive procedures 29—31
Reduction to tridiagonal form 95
Remes algorithms 266 et seq.
Resultant 198
Resultant, procedures 185
Rhombus rules 38
Romberg’s method 133
Romberg’s method, error analysis 135
Root squaring 192
Rounding errors 75
RSSR routine 185
Schoenberg’s theorem 159
Schur norm 67
Secant method 172 189 275
Second algorithm of Remes 267
Serial correlation 253
Shift of origin 118
Spectral condition number 74
Spline functions 156 et seq.
Spline functions, knots of 157
Spline functions, natural 157
Spline interpolation 158
Stability 122 137
Starting algorithm 269
Steady-state iteration 230—233
Sturm sequence 97
Subresultant 203 204
Successive overrelaxation 163
Sylvester’s determinant 198
Synthetic division 187
Systems of nonlinear equations 180—181
Transcendental equations 171 et seq.
Trapezoidal rule 134
Triangularization 69
Triangularization, Householder 81
Triangularization, orthogonal 72
Tridiagonal matrix 95 233
Tridiagonal matrix, eigenvalues of 96
Tridiagonal matrix, eigenvectors of 98
Tridiagonal matrix, reduction to 95
Tschebycheff quadrature 137—139
Unisolvent functions 267
Upper triangular matrix 69
Variables, ALGOL 9
Variables, FORTRAN 9
Weight function 145 264
Wielandt iteration 95
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