Matrix computations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Baltimore
The Johns Hopkins University Press
2013
|
| Ausgabe: | Fourth edition |
| Schriftenreihe: | Johns Hopkins studies in the mathematical sciences
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxi, 756 Seiten Illustrationen |
| ISBN: | 9781421407944 1421407949 |
Internformat
MARC
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|---|---|---|---|
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| 020 | |a 1421407949 |c hbk. |9 1-4214-0794-9 | ||
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| 100 | 1 | |a Golub, Gene H. |d 1932-2007 |e Verfasser |0 (DE-588)120319713 |4 aut | |
| 245 | 1 | 0 | |a Matrix computations |c Gene H. Golub (Department of Computer Science, Stanford University), Charles F. Van Loan (Department of Computer Science, Cornell University) |
| 250 | |a Fourth edition | ||
| 259 | |a 4 | ||
| 264 | 1 | |a Baltimore |b The Johns Hopkins University Press |c 2013 | |
| 300 | |a xxi, 756 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Johns Hopkins studies in the mathematical sciences | |
| 650 | 0 | 7 | |a Matrix |g Mathematik |0 (DE-588)4037968-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 220 G629(4) |
| DE-BY-FWS_katkey | 559483 |
| DE-BY-FWS_media_number | 083000515039 |
| _version_ | 1811222242169716736 |
| adam_text |
Contents
Preface
xi
Global
References
xiii
Other Books
xv
Useful URLs
xix
Common Notation
xxi
Matrix Multiplication
1.1
Basic Algorithms and Notation
2
1.2
Structure and Efficiency
14
1.3
Block Matrices and Algorithms
22
1.4
Fast Matrix-Vector Products
33
1.5
Vectorization and Locality
43
1.6
Parallel Matrix Multiplication
49
2.
Matrix Analysis
63
2.1
Basic Ideas from Linear Algebra
64
2.2
Vector Norms
68
2.3
Matrix Norms
71
2.4
The Singular Value Decomposition
76
2.5
Subspace Metrics
81
2.6
The Sensitivity of Square Systems
87
2.7
Finite Precision Matrix Computations
93
ó
General Linear Systems
105
3.1
Triangular Systems
106
3.2
The
LU
Factorization 111
3.3
Roundoff Error in Gaussian Elimination
122
3.4
Pivoting
125
3.5
Improving and Estimating Accuracy
137
3.6
Parallel
LU
144
τ-
Special Linear Systems
153
4.1
Diagonal Dominance and Symmetry
154
4.2
Positive Definite Systems
159
vii
viii
Contents
4.3
Banded Systems
176
4.4
Symmetric Indefinite Systems
186
4.5
Block Tridiagonal Systems
196
4.6
Vandermonde Systems
203
4.7
Classical Methods for Toeplitz Systems
208
4.8
Circulant
and Discrete
Poisson
Systems
219
O
Orthogonalization and Least Squares
233
5.1
Householder and
Givens
Transformations
234
5.2
The QR Factorization
246
5.3
The Full-Rank Least Squares Problem
260
5.4
Other Orthogonal Factorizations
274
5.5
The Rank-Deficient Least Squares Problem
288
5.6
Square and Underdetermined Systems
298
Ό
Modified Least Squares Problems and Methods
303
6.1
Weighting and Regularization
304
62
Constrained Least Squares
313
6.3
Total Least Squares
320
6.4
Subspace Computations with the
SVD
327
6.5
Updating Matrix Factorizations
334
í
Unsymmetric Eigenvalue Problems
347
7.1
Properties and Decompositions
348
7.2
Perturbation Theory
357
7.3
Power Iterations
365
7.4
The
Hessenberg
and Real
Schur
Forms
376
7.5
The Practical QR Algorithm
385
7.6
Invariant Subspace Computations
394
7.7
The Generalized Eigenvalue Problem
405
7.8
Hamiltonian and Product Eigenvalue Problems
420
7.9
Pseudospectra
426
8
Symmetric Eigenvalue Problems
439
8.1
Properties and Decompositions
440
8.2
Power Iterations
450
8.3
The Symmetric QR Algorithm
458
8.4
More Methods for Tridiagonal Problems
467
8.5
Jacobi Methods
476
8.6
Computing the
SVD
486
8.7
Generalized Eigenvalue Problems with Symmetry
497
Contents
ix
Functions of Matrices
513
9.1
Eigenvalue Methods
514
9.2
Approximation Methods
522
9.3
The Matrix Exponential
530
9.4
The Sign, Square Root, and Log of a Matrix
536
10
Large Sparse Eigenvalue Problems
545
10.1
The Symmetric Lanczos Process
546
10.2
Lanczos, Quadrature, and Approximation
556
10.3
Practical Lanczos Procedures
562
10.4
Large Sparse
SVD
Frameworks
571
10.5
Krylov Methods for Unsymmetric Problems
579
10.6
Jacobi-Davidson and Related Methods
589
A J. Large Sparse Linear System Problems
597
11.1
Direct Methods
598
11.2
The Classical Iterations
611
11.3
The Conjugate Gradient Method
625
11.4
Other Krylov Methods
639
11.5
Preconditioning
650
11.6
The Multigrid Framework
670
LZ. Special Topics
681
12.1
Linear Systems with Displacement Structure
681
12.2
Structured-Rank Problems
691
12.3 Kronecker
Product Computations
707
12.4
Tensor Unfoldings and Contractions
719
12.5
Tensor Decompositions and Iterations
731
Index
747 |
| any_adam_object | 1 |
| author | Golub, Gene H. 1932-2007 Van Loan, Charles F. |
| author_GND | (DE-588)120319713 (DE-588)172431484 |
| author_facet | Golub, Gene H. 1932-2007 Van Loan, Charles F. |
| author_role | aut aut |
| author_sort | Golub, Gene H. 1932-2007 |
| author_variant | g h g gh ghg l c f v lcf lcfv |
| building | Verbundindex |
| bvnumber | BV040720855 |
| classification_rvk | QH 140 SK 220 SK 915 |
| classification_tum | MAT 150 DAT 532 |
| ctrlnum | (OCoLC)835290390 (DE-599)GBV735104220 |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| edition | Fourth edition |
| format | Book |
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| id | DE-604.BV040720855 |
| illustrated | Illustrated |
| indexdate | 2024-09-26T04:02:13Z |
| institution | BVB |
| isbn | 9781421407944 1421407949 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025701078 |
| oclc_num | 835290390 |
| open_access_boolean | |
| owner | DE-634 DE-29T DE-91G DE-BY-TUM DE-83 DE-573 DE-739 DE-473 DE-BY-UBG DE-29 DE-11 DE-703 DE-862 DE-BY-FWS DE-20 DE-858 DE-523 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-521 DE-898 DE-BY-UBR DE-706 |
| owner_facet | DE-634 DE-29T DE-91G DE-BY-TUM DE-83 DE-573 DE-739 DE-473 DE-BY-UBG DE-29 DE-11 DE-703 DE-862 DE-BY-FWS DE-20 DE-858 DE-523 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-521 DE-898 DE-BY-UBR DE-706 |
| physical | xxi, 756 Seiten Illustrationen |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | The Johns Hopkins University Press |
| record_format | marc |
| series2 | Johns Hopkins studies in the mathematical sciences |
| spellingShingle | Golub, Gene H. 1932-2007 Van Loan, Charles F. Matrix computations Matrix Mathematik (DE-588)4037968-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Datenverarbeitung (DE-588)4011152-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Matrizenrechnung (DE-588)4126963-9 gnd |
| subject_GND | (DE-588)4037968-1 (DE-588)4042805-9 (DE-588)4011152-0 (DE-588)4128130-5 (DE-588)4126963-9 |
| title | Matrix computations |
| title_auth | Matrix computations |
| title_exact_search | Matrix computations |
| title_full | Matrix computations Gene H. Golub (Department of Computer Science, Stanford University), Charles F. Van Loan (Department of Computer Science, Cornell University) |
| title_fullStr | Matrix computations Gene H. Golub (Department of Computer Science, Stanford University), Charles F. Van Loan (Department of Computer Science, Cornell University) |
| title_full_unstemmed | Matrix computations Gene H. Golub (Department of Computer Science, Stanford University), Charles F. Van Loan (Department of Computer Science, Cornell University) |
| title_short | Matrix computations |
| title_sort | matrix computations |
| topic | Matrix Mathematik (DE-588)4037968-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Datenverarbeitung (DE-588)4011152-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Matrizenrechnung (DE-588)4126963-9 gnd |
| topic_facet | Matrix Mathematik Numerische Mathematik Datenverarbeitung Numerisches Verfahren Matrizenrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025701078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT golubgeneh matrixcomputations AT vanloancharlesf matrixcomputations |
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