Holdings: Matrix computations

Matrix computations:

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Bibliographic Details
Main Authors:	Golub, Gene H. 1932-2007 (Author), Van Loan, Charles F. (Author)
Format:	Book
Language:	English
Published:	Baltimore [u.a.] Johns Hopkins Univ. Press 1996
Edition:	3. ed.
Series:	Johns Hopkins studies in the mathematical sciences
Subjects:	Datenverarbeitung Matrices > Data processing Numerische Mathematik Matrizenrechnung Numerisches Verfahren Matrix > Mathematik
Online Access:	Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	XXVII, 694 S. graph. Darst.
ISBN:	080185413X 0801854148 9780801854149 0801837391

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MARC


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adam_text	Contents Preface to the Third Edition xi Software xiii Selected References xv A Matrix Multiplication Problems 1 1.1 Basic Algorithms and Notation 2 1.2 Exploiting Structure 16 1.3 Block Matrices and Algorithms 24 1.4 Vectorization and Re-Use Issues 34 2à Matrix Analysis 48 2.1 Basic Ideas from Linear Algebra 48 2.2 Vector Norms 52 2.3 Matrix Norms 54 2.4 Finite Precision Matrix Computations 59 2.5 Orthogonality and the SVD 69 2.6 Projections and the CS Decomposition 75 2.7 The Sensitivity of Square Linear Systems 80 О General Linear Systems 87 3.1 Triangular Systems 88 3.2 The LU Factorization 94 3.3 Roundoff Analysis of Gaussian Elimination 104 3.4 Pivoting 109 3.5 Improving and Estimating Accuracy 123 vii viii Contents 4 Special Linear Systems 133 4.1 The LDM11 and LDL·1 Factorizations 135 4.2 Positive Definite Systems 140 4.3 Banded Systems 152 4.4 Symmetric Indefinite Systems 161 4.5 Block Systems 174 4.6 Vandermonde Systems and the FFT 183 4.7 Toeplitz and Related Systems 193 õ Orthogonalization and Least Squares 206 5.1 Householder and Givens Matrices 208 5.2 The QR Factorization 223 5.3 The Full Rank LS Problem 236 5.4 Other Orthogonal Factorizations 248 5.5 The Rank Deficient LS Problem 256 5.6 Weighting and Iterative Improvement 264 5.7 Square and Underdetermined Systems 270 U Parallel Matrix Computations 275 6.1 Basic Concepts 276 6.2 Matrix Multiplication 292 6.3 Factorizations 300 í The Unsymmetric Eigenvalue Problem 308 7.1 Properties and Decompositions 310 7.2 Perturbation Theory 320 7.3 Power Iterations 330 7.4 The Hessenberg and Real Schur Forms 341 7.5 The Practical QR Algorithm 352 7.6 Invariant Subspace Computations 362 7.7 The QZ Method for Ax = λ Bx 375 О The Symmetric Eigenvalue Problem 391 8.1 Properties and Decompositions 393 8.2 Power Iterations 405 Contents ix 8.3 The Symmetric QR Algorithm 414 8.4 Jacobi Methods 426 8.5 Tridiagonal Methods 439 8.6 Computing the SVD 448 8.7 Some Generalized Eigenvalue Problems 461 У Lanczos Methods 470 9.1 Derivation and Convergence Properties 471 9.2 Practical Lanczos Procedures 479 9.3 Applications to Ax = b and Least Squares 490 9.4 Arnoldi and Unsymmetric Lanczos 499 1U Iterative Methods for Linear Systems 508 10.1 The Standard Iterations 509 10.2 The Conjugate Gradient Method 520 10.3 Preconditioned Conjugate Gradients 532 10.4 Other Krylov Subspace Methods 544 11 Functions of Matrices 555 11.1 Eigenvalue Methods 556 11.2 Approximation Methods 562 11.3 The Matrix Exponential 572 12 Special Topics 579 12.1 Constrained Least Squares 580 12.2 Subset Selection Using the SVD 590 12.3 Total Least Squares 595 12.4 Computing Subspaces with the SVD 601 12.5 Updating Matrix Factorizations 606 12.6 Modified/Structured Eigenproblems 621 Bibliography 637 Index 687
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author	Golub, Gene H. 1932-2007 Van Loan, Charles F.
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indexdate	2025-02-20T06:42:38Z
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isbn	080185413X 0801854148 9780801854149 0801837391
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-007568738
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open_access_boolean
owner	DE-20 DE-29T DE-739 DE-384 DE-703 DE-92 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-945 DE-19 DE-BY-UBM DE-1046 DE-355 DE-BY-UBR DE-634 DE-83 DE-11 DE-188 DE-M100 DE-863 DE-BY-FWS DE-706 DE-473 DE-BY-UBG
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physical	XXVII, 694 S. graph. Darst.
publishDate	1996
publishDateSearch	1996
publishDateSort	1996
publisher	Johns Hopkins Univ. Press
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series2	Johns Hopkins studies in the mathematical sciences
spellingShingle	Golub, Gene H. 1932-2007 Van Loan, Charles F. Matrix computations Datenverarbeitung Matrices Data processing Numerische Mathematik (DE-588)4042805-9 gnd Matrizenrechnung (DE-588)4126963-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Matrix Mathematik (DE-588)4037968-1 gnd Datenverarbeitung (DE-588)4011152-0 gnd
subject_GND	(DE-588)4042805-9 (DE-588)4126963-9 (DE-588)4128130-5 (DE-588)4037968-1 (DE-588)4011152-0
title	Matrix computations
title_auth	Matrix computations
title_exact_search	Matrix computations
title_full	Matrix computations Gene H. Golub ; Charles F. VanLoan
title_fullStr	Matrix computations Gene H. Golub ; Charles F. VanLoan
title_full_unstemmed	Matrix computations Gene H. Golub ; Charles F. VanLoan
title_short	Matrix computations
title_sort	matrix computations
topic	Datenverarbeitung Matrices Data processing Numerische Mathematik (DE-588)4042805-9 gnd Matrizenrechnung (DE-588)4126963-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Matrix Mathematik (DE-588)4037968-1 gnd Datenverarbeitung (DE-588)4011152-0 gnd
topic_facet	Datenverarbeitung Matrices Data processing Numerische Mathematik Matrizenrechnung Numerisches Verfahren Matrix Mathematik
url	http://www3.ub.tu-berlin.de/ihv/000310042.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007568738&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT golubgeneh matrixcomputations AT vanloancharlesf matrixcomputations

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