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Ralston A., Wilf H.S. — Mathematical methods for digital computers
Ralston A., Wilf H.S. — Mathematical methods for digital computers

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Название: Mathematical methods for digital computers

Авторы: Ralston A., Wilf H.S.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1967

Количество страниц: 302

Добавлена в каталог: 17.02.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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