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| Авторизация |
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| Gloub G.H., Ortega J.M. — Scientific Computing and Differential Equations |
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| Предметный указатель |
 norm 317
Adams — Bashforth methods 45ff
Adams — Moulton methods 47ff 156
Adjoint equation 163
Aho, A. 14 321
Allgower E. 176 321
Alternating direction method 281
Ames, W. 261 321
Anderson, E. 14 131 231 322
Arioli, M. 131 321
Arrowhead matrix 286ff
Ascher, U. 78 79 149 185 209 321
Asymptotically stable solution 217
Automatic differentiation 174
Axelsson, O. 282 321
B-spline 203ff
Back substitution 102ff
Backward differentation formula 64
Backward error analysis 8 115
Backward Euler method 62
Bai, Z. 322
Bailey, D. 110
Bairstow's method 163
Balancing 117
Ballistics problem 16
Banded matrix 106 118
Bandwidth 106
Barker, V. 282 321
Bartlett, M. 86
Basis functions 179
Becker, E. 282 321
Benzon, W. 14
Bidiagonal matrix 108
Bischof, C. 322
Bisection method 150
Block tridiagonal matrix 278
Boundary condition 4 248
Boundary-value problem 67ff
Boundary-value problem, nonlinear 171
Boyle, J. 323
Bramble, J. 77 321
Brenan, K. 36 321
Briggs, W. 305 321
Brown, P. 64 321
Bunch — Kaufman algorithm 141
Bunch, J. 322
Butcher, J. 35 36 53 64 322
Byrne, G. 64 321
Campbell, S. 36 321
Carey, G. 282 321 322
Catastrophic cancellation 8
Chain rule 309
Char, B. 14 322
Characteristic equation 58
Characteristic polynomial 211 314
Cholesky factorization 133 285
Chord method 154
Collocation 180ff 202ff
Companion matrix 163 223
Complete pivoting 119
Composite formulas 197ff
Computational complexity 10
Computational engineering 1
Computational science 1
Computer science 3
Condition number 128ff
Conjugate gradient method 300ff
Conjugate gradient method, preconditioned 301
Conjugate vectors 301
Consistency 53 255 295
Consistently ordered matrix 298
Continuation method 175
Convergence error 9
Convergence factor 159
Convergence theory 154ff 168ff
Convex function 157
Courant, R. 252 322
Crank — Nicolson method 264
Crout form 105
Cubic spline 189ff
Cyclic reduction algorithm 290
Dahlquist, G. 64
Daniel, J. 35 322
Data management 13
Davenport, S. 36 153 326
Davidenko's method 175
Davis, P. 201 322
deBoor, C. 193 209 322
Deferred correction 77
Deflation 236
Demmel, J. 321 322
Dennis, J. 174 322
Determinant 109 124
Diagonal matrix 316
Diagonally dominant matrix 72 118 120 173 295
Difference equation 57ff
Differential equation 311ff
Differential-algebraic system 36
Diffusion equation 247
Direction vector 300
Dirichlet boundary condition 75 275
Discretization error 8 23ff 48ff 70ff 254ff 264
Domain decomposition 286
Dongarra, J. 14 131 231 322 323
Doolittle form 105
DuCroz, J. 322
Duff, I. 14 290 321 322
Edelman, A. 120 322
Efficiency 9
Eigenvalue 211 314
Eigenvalue problem 211
Eigenvalue problem, generalized 216 231
Eigenvalue, ill conditioned 220
Eigenvector 211 314
Eigenvector, computation of 229ff 236ff
EISPACK 11 14 231
Elementary reflection matrix 137
Elliptic equation 247 252
Elliptic norm 317
Elmasri, R. 14 322
Equilibration 116
Erisman, A. 322
Euler equation 185
Euler's method 22ff 61 199 268
Explicit method 48 253ff
Fast Fourier Transform 290
Fast Poisson solver 290
fill 283
Finite difference method 21 67ff
Finite element method 282
Fischer, C. 14 322
Fix, G. 185 209 282 326
Forsythe, G. 282 323
FORTRAN 12
Forward reduction 102ff
Fourier series 251
Francis, J. 231 323
Friedhoff, R. 14 323
Frobenius matrix 223
Galerkin method 181ff 206ff
Garabedian, P. 252 323
Garbow, B. 14 231 323
Gauss — Seidel method 292
Gaussian elimination 81ff 101ff 283ff
Gaussian quadrature 200
Gear, C.W. 53 64 323
Geddes, K. 322
Geometric convergence 159
Georg, K. 176 321
George, A. 289 323
| Gerschgorin's theorem 217ff
Givens transformation 135
Givens, J. 231
Global convergence 157
Golub, G. 100 110 119 132 141 221 231 244 305
Gonnet, G. 322
Gordon, M. 326
Gould, N. 120 323
Gradient vector 310
Greenbaum, A. 322
Gregory, R. 44 327
Grid points 21 68
Griewank, A. 174 323
Gross, G. 20 326
Haberman, R. 252 323
Hackbrush, W. 305 323
Hageman, L. 303 323
Hager, W. 86 323
Hairer, E. 35 36 324
Hall, C. 186 209 261 282 324
Hammerling, S. 322
Hankel matrix 92
Hanson, R. 100 141 325
Hat function 207
Heat equation 247ff 253ff 273ff 279ff
Hennessy, J. 14 324
Henrici, P. 35 53 63 324
Hessenberg matrix 121 225ff 238
Hestenes, M. 305 324
Heun method 26ff
Higham, N. 110 324
Higher-order differences 77
Hilbert matrix 127
Hilbert, D. 252 322
Hindmarsh, A. 52 64 321 324
Hockney, R. 290 324
Householder reduction 138ff
Householder transformation 137 226
Householder — John theorem 304
Householder's method 229
Householder, A. 221 231 324
Hubbard, B. 77 321
Hyperbolic equation 247 252 269
IEEE standard 12
Ill-conditioning 8 56 122ff 161
Implicit method 48 262ff
Incomplete Cholesky factorization 302
Initial condition 4 16 248
Inner product 317
Instability 113ff 147ff
Interchanges 112ff
Interpolation 37ff
Interpolation error 39
Interval of uncertainty 151
Inverse 109
Inverse iteration 236
Irreducible matrix 78
Irreducibly diagonally dominant matrix 79
Isaacson, E. 261 324
Iterative refinement 131
Jacobi's method 230 292
Jacobian matrix 168
Jesshope, C. 290 324
Jordan elimination 112
Jordan form 214ff 304
Keener, J. 252 324
Keller, H. 79 261 324
Kublanovskaya, V. 231 324
Lagrange polynomials 38
Laguerre's method 163
Lanczos' method 241ff
LAPACK 11 14 130 131 231
Laplace's equation 247
Large sparse matrix 279
Lax equivalence theorem 258
Least squares problems 89ff 139ff
Linear convergence 159
Linear multistep methods 49
Linearly independent eigenvectors 212ff
LINPACK 11 14 130 131
Lotka — Volterra equation 16
LU factorization 103ff 112 285
Macsyma 13
Mai, T. 303 327
Maintainability 11
Maple 13
Mathematica 13
Mathematical model 3
Mathematical model, validation 5
Mathematics 3
MATLAB 11 14
Matrix norm 319
Mattheij, R. 321
McKenney, A. 322
Mean value theorem 309 310
Mendez, R. 14 325
Method of lines 271ff
Method of undetermined coefficients 199
Meyer, G. 14 325
Mid-point rule 37 194ff
Milne's method 64
Minimization 175
Minimum degree algorithm 289
Mixed-type equation 252
Modeling 4
Moler, C. 231 322 323 325
Moore, R. 35 322
More, J. 174 322
Morrison, W. 86
Morton, K. 261 265 282 325
Multigrid method 304
Multistep method 45ff 154
Murnaghan — Wintner theorem 215
Natural cubic spline 189
Natural ordering 277
Navathe, S. 14 322
Nested dissection 288
NETLIB 14
Neumann boundary condition 75 275
Newman, W. 14 325
Newton form of interpolation 42
Newton — Cotes formulas 194ff
Newton's method 153ff 168ff 232
Newton, R. 20 326
Nonlinear equations 145ff 184ff
Nonsingular matrix 315
Norm 128 317
Norm equivalence theorem 319
Normal equations 92
Norsett, S. 35 324
Numerical analysis 2
Numerical integration 193ff
Numerical mathematics 2
Oden, J. 282 321 322
ODEPACK 52
Ohlrich, M. 120 322
One-sided differences 73
One-step method 20ff 27ff 154 295
One-way dissection 288
Operation count 82 105 107 109 136 138
Order of method 28
Ortega, J. 63 79 119 174 176 221 232 290 304 305 325
Orthogonal functions 182
Orthogonal matrix 134ff 318
Orthogonal polynomials 94ff
Orthogonal vectors 318
Ostrowski theorem 298
Ostrowski — Reich theorem 304
Parabolic equation 247 252
Parallel computer 12
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