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Golub G.H., van Loan C.F. — Matrix Computations

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Название: Matrix Computations

Авторы: Golub G.H., van Loan C.F.

Аннотация:

This third edition offers expanded treatment of areas such as CS decomposition, floating point arithmetic, special linear systems, the unsymmetric Lanczos process, and Toeplitz matrix eigenproblems. Other changes to this edition include some 300 new references and 100 new problems, replacement of LINPACK and EISPACK citations with pointers to LAPACK with key codes tabulated at the beginning of appropriate chapters, and correction of the large number of typographical errors in the previous edition. Copyright © 1999 Book News, Inc., Portland, OR All rights reserved — This text refers to an out of print or unavailable edition of this title.

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Рубрика: Математика/Численные методы/Численная линейная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 1996

Количество страниц: 694

Добавлена в каталог: 21.02.2005

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

Предметный указатель

Principal angles and vectors      603—604
Processor id      276
Procrustes problem      601
Projections      75
Pseudo-eigenvalues      576—577
Pseudo-inverse      257
qmr      551
QR algorithm for eigenvalues, symmetric version      414ff
QR algorithm for eigenvalues, unsymmetric version      352ff
QR factorization      223ff
QR factorization, Block Householder computation      225—226
QR factorization, classical Gram — Schmidt and      230—231
QR factorization, column pivoting and      248—250 591
QR factorization, Fast Givens computation of      228—229
QR factorization, Givens computation of      226—227
QR factorization, Hessenberg matrices and      227—228
QR factorization, Householder computation of      224—225
QR factorization, least square problem and      239—242
QR factorization, Modified Gram — Schmidt and      231—232
QR factorization, properties of      229—230
QR factorization, rank of matrix and      248
QR factorization, square systems and      270—271
QR factorization, tridiagonal matrix and      417
QR factorization, underdetermined systems and      271—272
QR factorization, updating      607—613
Quadratic form      394
QZ algorithm      384ff
R-bidiagonalisation      552—553
RANGE      49
Rank deficient LS problem      256ff
Rank of matrix      49
Rank of matrix, determination of      259
Rank of matrix, QR factorization and      248
Rank of matrix, subset selection and      591—594
Rank of matrix, SVD and      72—73
Rank-one modification of diagonal matrix      442—444
Rank-one modification, eigenvalues and      397
Rank-one modification, QR factorization and      607—613
Rayleigh quotient iteration      408—409
Rayleigh quotient iteration, QR algorithm and      422
Rayleigh quotient iteration, symmetric-definite pencils and      465
Re      14
Real Schur decomposition      341
Real Schur decomposition, generalized      377
Rectangular LU      102
recv      277
Relaxation parameter      514
Residuals vs. accuracy      124
Restarting, Arnoldi method and      501—503
Restarting, GMRES and      549
Restarting, Lanczos and      584
Ridge regression      583—585
Ring      276
Ring algorithms, Cholesky      300—303
Ring algorithms, Jacobi eigensolver      434
Ritz, acceleration      334
Ritz, pairs and Arnoldi method      500
Ritz, pairs and Lanczos method      475
Rotation of subspaces      601
Rounding errors      see “Particular algorithm”
Roundoff error analysis      62—67
Row addition or deletion      610—611
Row partition      6
Row scaling      125
Row weighting in LS problem      265
S-step Lanczos      487
saxpy      4 5
Scaling and squaring for exp(.A)      573—574
Scaling, linear systems and      125
Schmidt orthogonalization      see “Gram — Schmidt”
Schur complement      103
Schur decomposition      313
Schur decomposition, generalized      377
Schur decomposition, matrix functions and      558—561
Schur decomposition, normal matrices and      313—314
Schur decomposition, real matrices and      341—342
Schur decomposition, symmetric matrices and      393
Schur decomposition, two-by-two symmetric      427—428
Schur vectors      313
Search directions      521ff
Secular equations      443 582
Selective orthogonalizaton      483—484
Semide finite systems      147—149
send      277
Sensitivity      see “Perturbation theory for”
SEP      325
Serious breakdown      505
Shared memory systems      285—289
Shared memory traffic      287
Sherman — Morrison formula      50
Shifts in QR algorithm      353 356
Shifts in QZ algorithm      382—383
Shifts in SVD algorithm      452
Shifts in symmetric QR algorithm      418—420
Sign function      372
Similarity transformation      311
Similarity transformation, condition of      317
Similarity transformation, nonunitary      314 317
Simpson’s rule      570
Simultaneous diagonalization      461—463
Simultaneous iteration      see “LR iteration orthogonal
Sine of matrix      566
Single shift QR iteration      354—345
Singular matrix      50
Singular value decomposition (SVD)      70—73
Singular value decomposition (SVD), algorithm for      253—234 448 452
Singular value decomposition (SVD), constrained least squares and      582—583
Singular value decomposition (SVD), generalized      465—467
Singular value decomposition (SVD), Lanczos method for      495—496
Singular value decomposition (SVD), Linear systems and      80
Singular value decomposition (SVD), null space and      71 602—603
Singular value decomposition (SVD), numerical rank and      260—262
Singular value decomposition (SVD), projections and      75

Singular value decomposition (SVD), proof of      70
Singular value decomposition (SVD), pseudo-inverse and      257
Singular value decomposition (SVD), rank of matrix and      71
Singular value decomposition (SVD), ridge regression and      583—585
Singular value decomposition (SVD), subset selection and      591—594
Singular value decomposition (SVD), subspace intersection and      604—605
Singular value decomposition (SVD), subspace rotation and      601
Singular value decomposition (SVD), total least squares and      596—598
Singular values, eigenvalues and      318
Singular values, interlacing properties      449—450
Singular values, minimax characterisation      449
Singular values, perturbation of      450—451
Singular vectors      70—71
span      49
Spectral radius      511
Spectrum      310
Speed-up      281
Splitting      511
Square root of a matrix      149
Static Scheduling      286
Stationary values      621
Steepest descent and conjugate gradients      520ff
Store by band      19—20
Store by block      45
Store by diagonal      21—23
Strassen method      31—33 66
Stride      38—40
Structure exploitation      16—24
Sturm sequences      440
SubMatrix      27
Subordinate norm      66
Subset selection      590
subspace      49
Subspace, angles between      603—604
Subspace, basis for      49
Subspace, deflating      381 386
Subspace, dimension      49
Subspace, distance between      76—77
Subspace, intersection      604—605
Subspace, invariant      372 307—403
Subspace, null space intersection      602—603
Subspace, rotation of      601
Successive over-relaxation (SOR)      514
Sweep      429
Sylvester equation      366—369
Sylvester law of inertia      403
sym.schur      427
Symmetric eigenproblem      391ff
Symmetric indefinite systems      161ff
Symmetric positive definite systems, Lanczos and      ff
Symmetric storage      20—22
Symmetric successive over-relaxation, (SSOR)      516—517
SYMMLQ      494
Taylor approximation of       565—567
Threshold Jacobi      436
Toeplitz matrix methods      193ff
Torus      276
Total least squares      595ff
Trace      310
Transformation matrices, Fast Givens      218—221
Transformation matrices, Gauss      94—95
Transformation matrices, Givens      215
Transformation matrices, Householder      209
Transformation matrices, Hyperbolic      611—612
Trench algorithm      199
Treppeniteration      335—336
Triangular matrices      93
Triangular matrices, multiplication between      17
Triangular matrices, unit      92
Triangular systems      88ff
Triangular systems, band      153—154
Triangular systems, multiple      91
Triangular systems, non-square      92
Tridiagonal matrices      416
Tridiagonal matrices, inverse of      537
Tridiagonal matrices, QR algorithm and      417ff
Tridiagonal systems      156—157
Tridiagonalization, Householder      414
Tridiagonalization, Krylov subspaces and      416
Tridiagonalization, Lanczos      472ff
ULV updating      613—618
Underdetermined systems      271—273
Underflow      61
Unit roundoff      61
Unit stride      38—40
Unitary matrix      73
Unreduced Hessenberg matrices      346
Unsymmetric eigenproblem      308ff
Unsymmetric Lanczos method      503—506
Unsymmetric positive definite systems      142
Updating the QR factorization      606—613
Vandermonde systems      183—188
Variance-covariance matrix      245—246
Vector computing, models      37
Vector computing, operations      4 36
Vector computing, pipelining      35—36
Vector length issue      37—38
Vector norms      52ff
Vector notation      4
Vector operations      4 36
Vector touch      41—42
Vectorization      34ff 157—158
Weighting, column      264—265
Weighting, row      586 (See also “Scaling”)
Wielandt — Hoffman theorem for eigenvalues      395
Wielandt — Hoffman theorem for singular values      450
Wilkinson shift      418
Work, least squares methods      263
Work, linear system methods      270
Work, SVD and      254
Workspace      23
Wrap mapping      278
WY representation      213—215
Yule — Walker problem      194

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