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Watkins D. — Fundamentals of matrix computations
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Название: Fundamentals of matrix computationsАвтор: Watkins D. Аннотация: A significantly revised and improved introduction to a critical aspect of scientific computation
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: second editionГод издания: 2002Количество страниц: 618Добавлена в каталог: 20.07.2005Операции: Положить на полку |
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84 85 Abel, N.H. 310 478 Absolute value of a matrix 159 176 acosh 450 Airfoil 69 Algebraic multiplicity 306 417 Ammar — Dillo conjecture 604 Angle between two vectors 186 Arnoldi process 435 Arnoldi process, implicitly restarted (IRA) 451 Arrowhead matrix 63 Augmented matrix 71 Back substitution 29 backslash 15 Backward error analysis 145 Backward stability 146 Backward stability and residual 146 463 Backward stability of Cholesky's method 164 Backward stability of forward substitution 159 Backward stability of Gaussian elimination 162 Backward stability of matrix multiplication 211 Backward stability of rotators and reflectors 206 211 Backward stability, componentwise 161 179 Backward stability, normwise 161 Band width 54 Banded matrix 54 Basis (of a subspace) 224 Bauer — Fike theorem 463 Bauer's Theorem 173 Best approximation theorem 243 583 bicg 600 BICGSTAB 599 Biconjugate-gradient (BiCG) algorithm 598 Bidiagonal matrix 402 Bidiagonal matrix, proper 405 Biorthogonal vectors 465 599 Bisection method 483 BLAS 102 Block Gaussian elimination 90 Block iteration 541 bucky 64 Bucky ball 64 Bulge-chasing algorithm 375 380 407 486 513 Bunch — Kaufman algorithm 106 Cache 10 Cancellation 144 Cancellation in Gaussian elimination 151 Catastrophic cancellation 144 Cauchy —Schwarz inequality 113 186 cgs 599 Characteristic equation 305 505 Characteristic polynomial 305 505 Chebyshev acceleration 550 Chebyshev polynomials 448 Chebyshev polynomials and convergence of CG algorithm 594 Chebyshev polynomials and convergence of Lanczos process 450 chol 39 Cholesky decomposition 34 Cholesky decomposition, downdating 253 255 257 Cholesky decomposition, updating 251 Cholesky's method, backward stability 164 Cholesky's method, block 45 Cholesky's method, bordered form 43 Cholesky's method, inner-product form 36 Cholesky's method, outer-product form 42 choline 581 Cofactor method 103 Column scaling 171 Column space 242 Companion matrix 309 Complete pivoting 104 Componentwise backward stability 179 Computer 148 cond 122 condeig 468 condest 132 Condition number 121 Condition number of nonsquare matrix 232 Condition number of simple eigenvalue 466 Condition number of simple eigenvector 471 Condition number of square matrix 121 Condition number, control of 284 Condition number, estimation of 131 Condition number, geometric view 123 128 Condition number, Skeel 177 Conductance 50 Conformable partition 9 Congruence 483 Congruence of matrix pairs 509 conjugate 208 Conjugate (vectors) 583 Conjugate transpose 49 Conjugate-gradient (CG) method 576 Conjugate-gradient (CG) method and Lanczos process 588 590 597 Conjugate-gradient (CG) method as acceleration technique 550 Conjugate-gradient (CG) method, convergence of 590 Conjugate-gradient (CG) method, derivation 581 Conjugate-gradient (CG) method, preconditioned 578 Contraction number 315 Convection-diffusion operator 107 109 Convergence rate, asymptotic ( 548 Convergence rate, of classical methods 549 Convergence ratio 315 Convergence, cubic 328 Convergence, linear 315 Convergence, quadratic 328 Convergence, slower than linear 315 cosh 450 cputime 5 Cramer's rule 105 Crout reduction 81 Cubic convergence 328 Cuppen's algorithm 491 Cuppen's algorithm, secular equation 494 Curse of dimensionality 529 Cuthill — McKee ordering, reverse 64 Damped iteration 553 Damped Jacobi method 544 Damped pendulum 299 Davidson's method 458 Decomposition, 84 479 Decomposition, 85 Decomposition, Cholesky 34 Decomposition, LDV 84 Decomposition, LR 482 Decomposition, LU 80 Decomposition, QR 190 Decomposition, Schur 337 Decomposition, singular value 262 Decomposition, spectral 339 Decomposition, twisted 489 Defective matrix 308 Deflation in the QR algorithm 361 delsq 68 demo 5 Departure from normality 468 Descent method 560 Descent method, CG 576 Descent method, Gauss — Seidel 561 Descent method, preconditioned CG 578 Descent method, SOR 562 Descent method, steepest 562 DET 104 Determinant, computation of 104 diag 220 Diagonal matrix 84 Diagonalization theorem 335 diary 5 Differential equations 289 502 Differential equations, asymptotically stable 298 Differential equations, homogeneous linear 291 Differential equations, nonhomogeneous linear 294 Differential equations, nonlinear 298 Differential equations, unstable 298 Dimension (of a subspace) 224 Direct sum (of subspaces) 241 Direct vs. iterative methods 310 Distance to nearest rank-deficient matrix 270 Distance to nearest singular matrix 274 Divide-and-conquer algorithm 491 Domain decomposition 549 Dominant eigenvalue 314 Doolittle reduction 81 Downdating QR, deleting a column 254 Downdating QR, deleting a row 252 Dqds algorithm 487 Duality in subspace iteration 428 EIG 300 504 Eigenpair 305 Eigenspace 414 Eigenvalue 305 505 Eigenvalue, condition number 466 Eigenvalues of normal matrices 345 Eigenvector 305 505 Eigenvector, condition number 471 Eigenvector, left 331 465 Eigenvector, right 465 eigs 452 Elementary row operation 71 Elimination, Gauss — Jordan 105 Elimination, Gaussian 71 elmat 70 Energy inner product and norm 582 Envelope of a matrix 57 EPS 169 Equivalence of linear systems 70 Equivalence of matrices 262 Equivalence of matrix pairs (pencils) 507 Equivalence, orthogonal 262 401 Error analysis, a priori vs. a posteriori 137 Error analysis, backward vs. forward 145 Error analysis, componentwise 175 Error, absolute vs. relative 141 Euclidean norm 112 Exact shift 323 367 Exceptional shift 367 eye 170 Fast Poisson solver 529 Fast rotators 194 Fill-in 63 Finite difference method 18 522 524 Five-point stencil 525 Floating-point, arithmetic 139 Floating-point, IEEE standard 140 FLOP 3 FORMAT 153 format, long 153 format, long e 500 format, short e 272 Fortran-90 101 Forward substitution 24 Forward substitution, backward stability 159 Forward substitution, block 30 Forward substitution, column oriented 27 Forward substitution, row oriented 24 Frobenius norm 115 full 322 Full rank 213 Fundamental subspaces 241 264 Galerkin condition 447 598 Galerkin condition, Petrov 599 gallery 70 Gauss transform 89 210 Gauss — Jordan elimination 105 Gauss — Seidel method 533 Gauss — Seidel method, as a descent method 561 Gauss — Seidel method, as smoother for multigrid 544 Gauss — Seidel method, block 541 Gauss — Seidel method, convergence rate 549 Gauss — Seidel method, line 542 Gauss — Seidel method, orderings 536 Gauss — Seidel method, red-black 537 Gauss — Seidel method, symmetric 538 Gaussian elimination, backward stability 162 Gaussian elimination, block 90 102 Gaussian elimination, column oriented 100 Gaussian elimination, generic 91 Gaussian elimination, inner-product formulation 81 Gaussian elimination, row oriented 100 Gaussian elimination, sparse 106 Gaussian elimination, with pivoting 93 Gaussian elimination, with small pivot 154 Gaussian elimination, without pivoting 71 Generalized eigenvalue problem 502 505 Generalized inverse, Moore — Penrose 277 Geometric multiplicity 342 417 Gerschgorin disk 473 Givens rotator 192 gmres 597 Gradient 560 Gram — Schmidt process, and QR decomposition 227 Gram — Schmidt process, classical 226—227 Gram — Schmidt process, modified 229 Gram — Schmidt process, reorthogonalization 233 Harmonic Ritz value 461 help 5 Hermitian matrix 49 337 hess 355 Hessenberg matrix 329 349 Hessenberg matrix, j-Hessenberg 460 Hessenberg matrix; 2-Hessenberg 379 Hessenberg matrix; proper (unreduced) 365 Hessenberg-triangular form 510 hilb 123 Hilbert matrix 123 150 248 Householder transformation 196 Hyperbolic transformation 256 Hyperplane 196 Ideal computer 142 Idempotent 195 Identity matrix 12 IEEE floating-point standard 140 Ill-conditioned matrix 121 Implicit-Q theorem 381 408 514 Implicitly restarted Amoldi (IRA) 451 Inductance 290 Induction, mathematical 31 Inertia 483 inf 148 Inner product 186 581—582 Inner product, complex 206 Inner product, energy 582 Inner product, induced by H 582 Inner product, of functions 247 INV 59 104 Invariant subspace 414 Inverse matrix 12 Inverse matrix, computation of 103 Inverse matrix, of a sparse matrix 59 Inverse matrix, pseudoinverse 277 Inverse power method (inverse iteration) 319 Invertible matrix 13 IRA 451 isieee 148 Isometric matrix (isometry) 221 issparse 67 Iterative refinement 178 Iterative vs. direct methods 310 Jacobi rotator 477 495
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