Golub G.H., van Loan C.F. — Matrix Computations :: Электронная библиотека попечительского совета мехмата МГУ

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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

      138
, conjugate gradients and      491—493
A-conjugate      522—523
A-norm      530
Aasen’s method      163—170
Absolute Value notation      62
Accumulated inner product      64
Algebraic multiplicity      316
Angles between subspaces      603
Approximation of a matrix function      562—570
Arnoldi factorization      500
Arnoldi method      499—503
Back-substitution      89—90 153
Backward error analysis      65—67
Backward successive over-relaxation      516
Balancing      360
Band algorithms, Cholesky      155—156
Band algorithms, Gaussian elimination      152—3
Band algorithms, Hessenberg LU      154—155
Band algorithms, triangular systems      153
Bandedness      16—17
Bandedness, data structures and      19—20 158—159
Bandedness, lower and upper      16
Bandedness, LU factorization and      152—153
Bandedness, pivoting and      154
Bandedness, profile      159
Bandwidth      16
Barrier      287
Bartels — Stewart algorithm      367
Basic solution in least squares      258—259
Basis      49
Basis, eigenvector      316
Basis, orthonormal      69
Bauer — Fike theorem      321
Biconjugate gradient method      550—551
Bidiagonal matrix      17
Bidiagonalization upper triangularizlng first      252—253
Bidiagonalization, Householder      251—253
Bidiagonalization, Lanczos      495—496
Big-Oh notation      13
Binary powering      569
Bisection      439
Bit reversal      190
Block algorithms, Cholesky      145—146
Block algorithms, cyclic reduction      177—180
Block algorithms, data re-use and      43
Block algorithms, diagonalization      366
Block algorithms, Gaussian elimination      116—117
Block algorithms, Jacobi      435
Block algorithms, Lanczos      485 505
Block algorithms, LU      101—102
Block algorithms, LU with pivoting      116—117
Block algorithms, matrix functions and      560—561
Block algorithms, QR factorization      213—214
Block algorithms, tridiagonal      174
Block algorithms, unsymmetric Lanczos      505
Block Householder      225
Block matrices      24ff
Block matrices, data re-use and      43—45
Block matrices, diagonal dominance of      175
Block Schur and matrix functions      560
Block vs.band      176
Bunch — Kaufman algorithm      169
Cache      41
Cancellation      61
Cauchy — Schwartz inequality      53
Cayley transform      73
CGNE      546
CGNR      545
Characteristic polynomial      310
Characteristic polynomial, generalized eigenproblem and      375—376
Chebyshev polynomials      475
Chebyshev semi-iterative method      514—516
Cholesky reduction of $A - \lambda B$       463—464
Cholesky, band      155—156
Cholesky, block      145—146
Cholesky, downdating and      611
Cholesky, gaxpy      143—144
Cholesky, outer product      144—145
Cholesky, ring      300—303
Cholesky, shared memory      303—304
Cholesky, stability      146
Chordal metric      378
Circulant systems      201—202
Classical Gram — Schmidt      230—231
Classical Jacobi iteration for eigenvalues      428—429
Colon notation      7 19
Column, deletion or addition in QR      608—610
Column, partitioning      6
Column, pivoting      248—250
Column, weighting in LS      264—265
Communication costs      277 280—281 287
Companion matrix      348
Complete, orthogonal decomposition      250—251
Complete, rank deficiency and      256
Complete, reorthogonalization      482—483
Complex, matrices      14
Complex, QR factorization      233
Computation tree      446
Computation/communication ratio      281
Condition number, estimation      128—130
Condition of eigenvalues      323—324
Condition of invariant subspaces      325
Condition of least squares problem      242—245
Condition of linear systems      80—82
Condition of multiple eigenvalues      324
Condition of rectangular matrix      230
Condition of similarity transformation      317
Confluent Vandermonde matrix      188
Conformal partition      25
Conjugate gradient method, derivation and properties      490—493 520—528
Conjugate gradient method, Lanczos and      528
Conjugate, directions      522—523
Conjugate, residual method      547—548
Conjugate, transpose      14
Consistent norms      55
Constrained least squares      580ff
Contour integral and f(A)      556
Convergence of bisection method      439
Convergence of Chebyshev semi-iterative method      515
Convergence of conjugate gradient algorithm      530
Convergence of cyclic Jacobi algorithm      430
Convergence of Gauss — Seidel iteration      511—512
Convergence of inverse iteration      408
Convergence of iterative methods      511
Convergence of Jacobi iteration      511—512
Convergence of Jacobi’s method for the symmetric eigenproblem      429
Convergence of Lanczos method      425—427
Convergence of orthogonal iteration, symmetric case      411
Convergence of power method (symmetric)      406—407
Convergence of QR algorithm      360
Convergence of QZ algorithm      386
Convergence of Rayleigh Quotient iteration      408—409
Convergence of steepest descent      520—521
Convergence of SVD algorithm      456
Convergence of symmetric QR iteration      421
Convergence of unsymmetric case      333 336—339
Cosine of a matrix      567
Courant — Fischer minimax theorem      394
Crawford number      463
Critical section      289
Cross-validation      584
Crout — Doolittle      104
CS decomposition      77—79
Cyclic Jacobi method      430
Cyclic reduction      177—180
Data re-use      34 41
Data structures, block      45
Data structures, diagonal      21—22
Data structures, distributed      278

Data structures, symmetric      20—22
Deadlock      280
Decomposition,       138
Decomposition,       136
Decomposition, Arnoldi      500
Decomposition, bidiagonal      251
Decomposition, block diagonal      315
Decomposition, Cholesky      143
Decomposition, companion matrix      348
Decomposition, complete orthogonal      250—251
Decomposition, CS (general)      78
Decomposition, CS (thin)      78
Decomposition, generalized real Schur      377
Decomposition, generalized Schur      377
Decomposition, Hessenberg      344
Decomposition, Hessenberg-triangular      378—380
Decomposition, Jordan      317
Decomposition, LQ      494
Decomposition, LU      97—98
Decomposition, PA=LU      113
Decomposition, QR      223
Decomposition, real Schur      341—342
Decomposition, Schur      313
Decomposition, singular value      70
Decomposition, singular value (thin)      72
Decomposition, Symmetric Schur      393
Decomposition, tridiagonal      414
Defective eigenvalue      316
Deflating subspace      381 386
Deflation and bidiagonal form      454
Deflation and Hessenberg-triangular form      381—382
Deflation and QR algorithm      352
Departure from normality      314
Derogatory matrix      349
Determinant      50—51 310
Determinant and singularity      82
Determinant, Gaussian elimination and      97
Determinant, Vandermonde matrix      191
Diagonal dominance      120
Diagonal dominance, block      175—176
Diagonal form      316
Diagonal pivoting method      168—169
Differentiation of factorizations      51 103 243 273 323
DIMENSION      49
Distance between subspaces      76—77
Distributed memory model      276—277
Divide and conquer algorithms, cyclic reduction      177—180
Divide and conquer algorithms, Strassen      31—33
Divide and conquer algorithms, tridiagonal eigenvalue      444—447
Domain decomposition      538—539
Dominant, eigenvalue      331
Dominant, eigenvector      331
Dominant, invariant subspace      333
Doolittle reduction      104
Dot product      5
Dot product roundoff      62
DOUBLE PRECISION      64
Doubling formulae      567
Durbin’s algorithm      195
Dynamically scheduled algorithms      288
Efficiency      281
Eigen problem, constrained      621
Eigen problem, diagonal plus rank-1      442
Eigen problem, generalized      375ff 461ff
Eigen problem, inverse      622—623
Eigen problem, orthogonal matrix      625—631
Eigen problem, symmetric      391ff
Eigen problem, Toeplitz      623—625
Eigen problem, unsymmetric      308ff
Eigenvalues, characteristic polynomial and      310
Eigenvalues, computing selected      440—441
Eigenvalues, defective      316
Eigenvalues, determinant and      310
Eigenvalues, dominant      331
Eigenvalues, generalized      375
Eigenvalues, interior      478
Eigenvalues, ordering In Schur form      365—366
Eigenvalues, sensitivity of (symmetric)      395—397
Eigenvalues, sensitivity of (unsymmetric)      320—324
Eigenvalues, simple      316
Eigenvalues, singular values and      318
Eigenvalues, Sturm sequence and      440—442
Eigenvalues, trace      310
Eigenvector, dominant      331
Eigenvector, left      311
Eigenvector, matrix and condition      323—324
Eigenvector, perturbation      326—327
Eigenvector, right      311
EISPACK      xiv
Elementary Hermitian matrices      see “Householder matrix”
Elementary transformations      see “Gauss transformations”
Equality constained least squares      585—587
Equilibration      125
Equilibrium systems      170—171
Equivalence of norms      53
Error estimation in power method      332
Error, absolute      53
Error, matrix function      563—564 566—567
Error, relative      53
Error, roundoff      61
Euclidean matrix norm      see “Frobenlus matrix norm”
Exchange matrix      193
Exponent range      60
Exponential of matrix      572ff
F-norm      55
Factorization      see “Decomposition”
Fast Fourier Transform      188—191
Fast Givens QR      218 228 241
fl      61
Floating point numbers      59
FLOP      18—19
Forward error analysis      65—66
Forward substitution      88 90 153
Francis QR Step      356—358
Frechet derivative      81
Frobenius matrix norm      55
Function of triangular matrix      558—561
Gauss transformations      95—96
Gauss transformations, Hessenberg form and      349
Gauss-Jordan transformations      103
Gauss-Seidel      510 512—513
Gauss-Seidel iteration, solving Poisson equation and      512—513
Gauss-Seidel iteration, use as preconditioner      540
Gaussian elimination      94ff
Gaussian elimination, accuracy and      123ff
Gaussian elimination, block version      101
Gaussian elimination, complete pivoting and      118
Gaussian elimination, gaxpy version      100
Gaussian elimination, outer product version      98
Gaussian elimination, partial pivoting and      110—113
Gaussian elimination, roundoff error and      104ff
Gaxpy algorithms, band Cholesky      156
Gaxpy algorithms, Cholesky      144
Gaxpy algorithms, Gaussian elimination      114—115
Gaxpy in distributed memory      279
Gaxpy in shared memory      286
Gaxpy vs. Outer Product      42
Generalized eigenproblem      375ff 461ff
Generalized least squares      266—267
Generalized Schur decomposition      377
Generalized singular value and constrained least squares      580—582
Generalized singular value, decomposition      465—467
Generalized singular value, proof of      466
Geometric multiplicity      316
Gershgorin circle theorem      320 395
Ghost eigenvalues      484—485
givens      216
Givens QR      226—227
Givens rotations      215—218
Global variables      285

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