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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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Предметный указатель
Jacobi — Davidson method 458 Jacobi — Davidson method, inexact solves 459 Jacobi — Davidson method, purging 459 Jacobi's method, block variant 541 Jacobi's method, convergence rate 549 Jacobi's method, damped 544 Jacobi's method, for eigenvalue problem 477 Jacobi's method, for linear system 531 Jacobian matrix 299 Jordan block 309 554 Jordan canonical form 335 554 Kahan matrix 149 273 Kalian 273 Kernel 241 Kirchhoff's laws, current 13 Kirchhoff's laws, voltage 15 kron 109 Kronecker product 556 Krylov matrix 390 446 Krylov subspace 436 585 Krylov Subspace Methods 596 Lanczos process 441 Lanczos process, connection with CG 588 590 597 LDV decomposition 84 Least squares problem 181 Least squares problem, and SVD 275 Least squares problem, continuous 247 Least squares problem, discrete 182 243 Least squares problem, solution in full-rank case 213 Least squares problem, solution in rank-deficient case 216 275 Line iteration 542 Line search 560 Line search, exact vs. inexact 561 linear combination 223 Linear convergence 315 Linear independence and dependence 224 Long 153 lotkin 153 Lotkin matrix 153 LR algorithm 485 lu 98 LU decomposition 80 luinc 600 m-file 5 Manhattan metric 114 Markov chain 332 Matrix norm 115 Matrix pencil (pair) 505 Matrix pencil (pair), eqnivalence 507 Matrix pencil (pair), symmetric 508 matrix-matrix multiplication 7 matrix-vector multiplication 5 Maxmag 123 Minimum-degree ordering, column 108 Minimum-degree ordering, symmetric 64 Minmag 123 Minres 597 Monk polynomial 309 Moore — Penrose generalized inverse 277 more 53 Multicolor ordering 537 Multigrid 544 549 Multigrid, damped Jacobi smoother 544 Multigrid, Gauss — Seidel smoother 544 Multiplication, matrix 6 Multiplication, matrix-vector 2 Multiplicity, algebraic 306 Multiplicity, algebraic vs. geometric 417 Multiplicity, geometric 342 NaN 148 NASA Airfoil 69 Nested-dissection ordering 69 Newton's second law 297 nnz 67 Nondefective matrix 308 Nonsingular matrix 13 Norm 112 Norm, energy 582 Norm, matrix 115 Norm, matrix, 119 Norm, matrix, Frobenius 115 Norm, matrix, induced 116 Norm, matrix, p-norm 118 Norm, matrix, spectral (2-norm) 118 Norm, matrix; 1-norm (column sum) 119 Norm, of a function 247 Norm, vector 112 Norm, vector, 114 Norm, vector, A-norm 115 Norm, vector, Euclidean (2-norm) 112 Norm, vector, p-norm 114 Norm, vector, taxicab (1-norm) 114 Norm, vector; 1-norm 114 Normal equations 244 Normal matrix 339 Null space 241 numgrid 68 Ohm's law 13 ones 153 Operator norm 116 Orthogonal complement 240 Orthogonal decomposition 273 Orthogonal eqnivalence 262 401 Orthogonal matrix 187 Orthogonal projection (of vector onto subspace) 240 Orthogonality of functions 247 Orthogonality of vectors 186 Orthonormal vectors 221 Orthoprojector 195 Overdetermined system 184 Overflow 140 Partial pivoting 94 Partition, conformable 9 peg 580 Pencil (pair) 505 Pencil (pair), equivalence 507 Pencil (pair), regular vs. singular 506 Pencil (pair), symmetric 508 Permntation matrix 97 187 Perron — Frobenius theory 331 Petrov — Galerkin conditions 599 pinv 280 Pivot 94 Pivoting, complete 104 Pivoting, partial 94 Plane rotator 192 plot 184 Poisson's equation 524 POLY 304 Positive definite matrix 33 Positive definite matrix, complex 49 Positive semidefinite matrix 344 Power method 314 Power method, convergence rate 315 Power method, inverse 319 Preconditioner 571 Preconditioner and Richardson's method 553 Preconditioner as splitting matrix 544 Preconditioner domain decomposition 575 Preconditioner incomplete factorization 575 581 Preconditioner, diagonal (= Jacobi) 573 Preconditioner, multigrid 575 Preconditioner, SSOR 574 Principal submatrix 43 72 print 300 Projector 195 Proper Hessenberg matrix 365 Pseudoinverse 277 purging 459 Pythagorean Theorem 243 qmr 599 qr 205 220 QR algorithm 356 QR algorithm, accelerating convergence by shifting 361 QR algorithm, as Rayleigh quotient iteration 430 QR algorithm, as simultaneous iteration 426 QR algorithm, deflation 361 QR algorithm, exact shift 367 QR algorithm, exceptional shift 367 QR algorithm, implicit vs. explicit 373 QR algorithm, implicit, double step 377 QR algorithm, implicit, single step 372 QR algorithm, on Hessenberg matrices 358 QR algorithm, Rayleigh quotient shift 362 QR algorithm, reduction 365 QR algorithm, singular case 367 QR algorithm, Wilkinson shift 364 QR algorithm, with symmetric matrix 377 QR decomposition 190 QR decomposition and Gram — Schmidt process 227 QR decomposition by reflectors 203 QR decomposition by rotators 193 QR decomposition, complex 208 QR decomposition, condensed 222 QR decomposition, nonsquare 213 QR decomposition, rank-deficient case 217 QR decomposition, uniqueness 204 223 QR decomposition, with column pivoting 217 QR iteration (QR step) 357 qrdelete 255 qrinsert 254 Quadratic convergence 328 Quasi-triangular matrix 341 Quotient-difference (QD) algorithm 485 Quotient-difference (qd) algorithm, differential form 487 QZ algorithm 511 rand 332 randn 5 randperm 68 RANGE 241 Rank 213 241 Rank-one update, eigenvalue problem 492 Rank-one update, of identity matrix 90 209 Rayleigh quotient 325 Rayleigh quotient iteration 326 Rayleigh quotient iteration, convergence rate 327 Rayleigh quotient iteration, cubic convergence 328 Rayleigh quotient iteration, in QR algorithm 430 Rayleigh quotient iteration, quadratic convergence 328 Rayleigh quotient, matrix 447 Rayleigh quotient, of normal matrix 345 Rayleigh quotient, shift 362 Rayleigh — Ritz — Galerkin condition 447 Red-black ordering 537 Refinement, iterative 178 Reflector 196 Reflector, backward stability 206 211 Reflector, complex 207 Regular pencil (pair) 506 Relatively robust representation (RRR) 480 Reorthogonalization 233 Residual 137 Residual and backward stability 146 463 Richardson's method 545 Ritz pair 439 Ritz value 439 447 Ritz value, harmonic 461 Ritz vector 439 447 Roots 304 Rotator 188 Rotator, backward stability 206 211 Rotator, complex 207 Rotator, fast 194 Rotator, Givens 192 Rotator, Jacobi 477 495 Rotator, plane 192 Roundoff error 140 Roundoff, unit 142 Row operation, elementary 71 Row scaling 171 Row space 242 RRR algorithm 488 rsEcsf 349 SAVE 54 Scaling 171 Scaling, bad 127 schur 349 Schur complement 48 90—91 258 Schur's theorem 337 Schur's theorem, generalized 509 517 Schur's theorem, real (Wintner — Murnaghan) 341 Schwarz inequality 113 186 Scientific notation 139 Secular equation 494 Semiband width 54 semicolon 6 semilogy 600 Semisimple matrix 308 Shift 319 Shift, exact 323 367 Shift, exceptional 367 Shift, Rayleigh quotient 362 Shift, ultimate 393 Shift, Wilkinson 364 Shift-and-invert strategy 319 Shift-and-invert strategy and Amoldi process 441 Shift-and-invert strategy and IRA 455 Shift-and-invert strategy and subspace iteration 434 Similar matrices 334 Similarity 334 Similarity, orthogonal and unitary 336 Simultaneous iteration 423 Simultaneous iteration on sparse matrices 433 Singular matrix 13 Singular pencil (pair) 506 Singular value decomposition (SVD) 262 Singular vectors 262 SIZE 67 Skeel condition number 177 Skew-Hermitian matrix 339 Skew-symmetric matrix 347 Slicing method 483 SOR method 539 SOR method, as a descent method 562 SOR method, block 541 SOR method, convergence rate 549 SOR method, line 542 SOR method, red-black 542 SOR method, symmetric 539 sort 445 Span of a set of vectors 223 Spanning set (of a subspace) 224 sparfun 64 Spectral norm 118 Spectral radius 547 Spectral theorem for Hermitian matrices 339 Spectral theorem for normal matrices 340 Spectral theorem for real symmetric matrices 340 Spectrum 305 speye 64 Splitting matrix (= preconditioner) 544 spy 65 Spy plot 65 SSOR 539 Stability, backward 146 Standard basis 221 Steepest descent method 562 Steepest descent method, geometric interpretation 565 Steepest descent method, preconditioned 572 Stiffness matrix 17 560
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