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| Авторизация |
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| Rice J. — Matrix computations and mathematical software |
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| Предметный указатель |
Acceptable solution 129
ACM Algorithms Distribution Service 177
Aird — Lynch estimate 92 94 116
Aird, T.J. 92 206 239
Algorithm selection problem 74
Algorithm space 75 81
Back substitution 10 34
Backward error analysis 121 123 127
Band matrix 27
Band matrix software 207 239
Band matrix solvers 161
BLAS 177 187 189
Block-Jacobi method 143
bounds 101 118 239
Boyle, J.M. 187—189 233
Buffer 49
Bunch, J.R. 187 203
Cholesky factorization 46 48
Column vector 5
Column-sum norm 11
Compiler effects 65
Complete pivoting 39
Component 6
Component suppression 142
Composite error estimator 115
Computational complexity 50
Condition number 91 113
Condition number computation 93
Condition number, natural 91
Condition number, standard 92
Condition of a computation 109
Condition of a problem 109 112
Condition of Ax = b 112
Condition of evaluating f(x) 113
Condition of integration 133
Condition, absolute 113
Condition, relative 113
Consistency 13
Convergence, iteration 139
Coordinate system 6
Cramer's rule 15
Criteria space 79 81
Crout algorithm 45 64
Crowder, H. 74
Decomposable matrices 30
Dembo, R.S. 74
Determinant 23
Diagonal dominance 42 139
Diagonal matrix 28
Differential equations 166
Differential equations, partial 141—142 167
Direct method 137
Dodson, David S. 237
Dongarra, J.J. 187 233
Dot product 6
Dritz, K. 187 189
Dynamic model 1
Eigensystem software 233
Eigenvalues 10 233
Eigenvector 10 233
EISPACK 233
Error analysis, backward 121 123 127
Error analysis, forward 121
Error analysis, Gauss elimination 129
Error estimate, comparison 98
Error estimate, composite 115
Faddeev, D.K. 143
Feature space 67 77 80
features 67 76
Finite differences 18 27 167
Forcing function 18
Forsythe, G.E. 142 206 211
Forward error analysis 121
Fox, L. 142
Fuzzy linear systems 129
Garbow, B.S. 233
Gauss elimination 9 33 36 42 118 127 164
Gauss elimination project 160 164
Gauss elimination, error analysis 129
Gauss — Seidel method 138 140 168 170 171
GELB 238
Givens transformation 153 180
Gram — Schmidt algorithm 151—152 172
Gram — Schmidt orthogonalization 149 164
Gram — Schmidt, modified 151—152 172 173
Hanson, R.J. 155 177 203 277
Hilbert matrix 89 98 101
Hilbert matrix, fuzzy analysis 131
Homogeneous system of equations 9
Householder transformation 154 216
Identity matrix 9
Ikebe, Y. 233
Ill-conditioned problem 111 168
Ill-conditioning 111
IMSL library 160—162 201
Inner product 6
Inverse 9 22 50
Iteration convergence 139
Iterative improvement 96 105
Iterative method 137 166 168 170
Jacobi method 137 139 170
Jordan elimination 169
Kincaid, D.R. 177
Klema, V.C. 233
Krough, F.T. 177
Language 53 161 162
Language, problem-oriented 54
Lawson and Hanson, Solving Least Squares Problems 155
Lawson, C.L. 155 177 203 227
Least squares 20 145 172 215 227
Least squares approximation 146
Least squares software 203 227
LEQT1B 207
LEQT1F 210
Library 55
Library software 56
Linear equation 9
Linear equation solver 59
Linear equation, overdetermined 146
Linear equation, software 60 67 160 166 189 202 217 237
Linear function 8 11
Linear independence 6
Linear least squares 145 172
Linear mapping 8
LINEQ1 237
LINEQ2 100—103
LINPACK 101 103 131 160—162 187
LINPACK, estimate 94
LU factorization 33
Lynch, R.E. 92 206 239
Machine problem 115
Magnification factor 40 42
Martin, R.S. 208
Mathematical language 53
Mathematical model 1 18 21 147
Mathematical software 53 112 162
Matrices, computational sensitivity 98
Matrix 8
Matrix equation 22
Matrix exponential function 15
Matrix identity 9
| Matrix norm 11
Matrix, diagonal 28
Matrix, inverse 9 22 50
Matrix, nonsingular 9
Matrix, orthogonal 10 29
Matrix, permutation 10 29
Matrix, positive-definite 28 42
Matrix, random 100 103
Matrix, reducible 30
Matrix, sparse 25 137
Matrix, symmetric 28 48
Matrix, triangular 29
Matrix, tridiagonal 27 29
Matrix, upper triangular 10
Model 1 17 21
Modified Gram — Schmidt 151—152 172 173
Moler, C.B. 187 206 211 233
Mulvey, J.M. 74
NAG (Numerical Algorithms Group) library 213
NASTRAN 54
Natural condition number 91
Nonsingular matrix 9
Norm 6 11
Normal equations 148
Numerical Algorithms Group (NAG) 213
Oettle, W. 129
Operating system schedulers 80
Operation count 48
Operation count, least-squares 148 151—152 155
Optimization 2
Organizational model 21
orthogonal matrices 10 29
Orthogonal matrices, matrix factorization 152
Orthogonal vector 6
Overflow 190
Partial differential equations 141—142 167
Partial pivoting 39 42
Partial pivoting, band matrices 161
Pei matrix 98
Performance criteria 79
Performance profile 69 166
Performance, evaluation 63 72 166
Performance, measure 75 81
Permutation 10
Permutation, matrices 10 29
Physical system model 17
Pivoting 38 64
Pivoting, complete 39
Pivoting, partial 39 42 161
Plane rotation 153 169 180
Portability 66 85
Positive semidefinite matrix 28
Positive-definite matrix 28 42
Prager, W. 129
Principal submatrices 33
Problem space 67 75 80
Problem space, library 55
Program proofs 69
Programming language 53 162
Programming language effects 161
Project reflection 169
Project robustness 165
Project rotations 169
Project, band matrices 161
Project, differential equations 166
Project, Gauss elimination 160 164
Project, Gauss — Seidel 168 170
Project, Gram — Schmidt 164 171
Project, ill-conditioning 168
Project, iterative methods 166 168 170
Project, Jacobi 170
Project, least-squares 172
Project, mathematical software 112
Project, performance evaluation 166
Project, programming language 161
Project, programming style 162
Project, software evaluation 166
Project, SOR 170
Purdue University 81 100
Purdue University Computing Center 235
QR-algorithm 233
random matrix 100 103
Reducible matrices 30
Reflection 154 169 216
Regression 20 89 145 147
Reinsch, C. 224 233
Reliability 55
Residual least-squares 156
Rice, John R. 113 151
Robustness 55 165
Romberg integration 165
Round-off polynomial, example 126
Row vectors 7
Row-sum norm 11
Scaling 43
Scheduling algorithm 81
Semi-iterative method 143
Sensitivity analysis 95 105
SGECO 198
SGEFA 199
SIGNUM (Special Interest Group for Numerical Mathematics) 177
Similarity transformation 12
Singular value analysis 155
Singularity test 36
Smith, B.T. 233
software design 59 189
software sources 235
software testing 66
Software, performance evaluation 63 166
SOR (systematic overrelaxation) method 141 170
Sparse matrices 25 137
Spectral radius 10
Standard condition number 92
Static model 1
Stationary iteration 139
Stewart, G.W. 180 187
Storage allocation 61
Symmetric matrix 28 48
TAMPR 187 189
Tchebycheff semi-iterative method 143
Tic-Tac-Toe 76
Tools for analysis 3
TRANSPOSE 6
Triangular matrix 29
Tridiagonal matrix 27 29
Underflow 190
Upper triangular matrix 10
Varga, R.S. 142
Variable dimensions 61
Vector 5
Vector basis 6
Vector column 5
Vector component 6
Vector row 7
Vector, orthogonal 6
Verifiable hypotheses 72
Wasow, W.R. 142
Well-conditioning 111
Wilkinson, J.H. 123 206 208 224 233
Wilkinson, J.H., 4x4 102
Wilkinson, J.H., 4x4, fuzzy analysis 130
Young, D.M. 142
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