Numerical matrix analysis linear systems and least squares
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
SIAM
2009
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| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1819789596616032256 |
|---|---|
| adam_text | Titel: Numerical matrix analysis
Autor: Ipsen, Ilse
Jahr: 2009
Contents
Preface ix
Introduction xiii
1 Matrices 1
1.1 What Is a Matrix? 1
1.2 Scalar Matrix Multiplication 4
1.3 Matrix Addition 4
1.4 Inner Product (Dot Product) 5
1.5 Matrix Vector Multiplication 6
1.6 Outer Product 8
1.7 Matrix Multiplication 9
1.8 Transpose and Conjugate Transpose 12
1.9 Inner and Outer Products, Again 14
1.10 Symmetric and Hermitian Matrices 15
1.11 Inverse 16
1.12 Unitary and Orthogonal Matrices 19
1.13 Triangular Matrices 20
1.14 Diagonal Matrices 22
2 Sensitivity, Errors, and Norms 23
2.1 Sensitivity and Conditioning 23
2.2 Absolute and Relative Errors 25
2.3 Floating Point Arithmetic 26
2.4 Conditioning of Subtraction 27
2.5 Vector Norms 29
2.6 Matrix Norms 33
2.7 Conditioning of Matrix Addition and Multiplication 37
2.8 Conditioning of Matrix Inversion 38
3 Linear Systems 43
3.1 The Meaning of Ax = b 43
3.2 Conditioning of Linear Systems 44
3.3 Solution of Triangular Systems 51
3.4 Stability of Direct Methods 52
3.5 LU Factorization 58
3.6 Cholesky Factorization 63
3.7 QR Factorization 68
3.8 QR Factorization of Tall and Skinny Matrices 73
4 Singular Value Decomposition 77
4.1 Extreme Singular Values 79
4.2 Rank 81
4.3 Singular Vectors 86
5 Least Squares Problems 91
5.1 Solutions of Least Squares Problems 91
5.2 Conditioning of Least Squares Problems 95
5.3 Computation of Full Rank Least Squares Problems 101
6 Subspaces 105
6.1 Spaces of Matrix Products 106
6.2 Dimension 109
6.3 Intersection and Sum of Subspaces 111
6.4 Direct Sums and Orthogonal Subspaces 115
6.5 Bases 118
Index 121
|
| any_adam_object | 1 |
| author | Ipsen, Ilse C. F. |
| author_GND | (DE-588)137389973 |
| author_facet | Ipsen, Ilse C. F. |
| author_role | aut |
| author_sort | Ipsen, Ilse C. F. |
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| building | Verbundindex |
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| dewey-full | 511/.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.42 |
| dewey-search | 511/.42 |
| dewey-sort | 3511 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV026751993 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T00:54:24Z |
| institution | BVB |
| isbn | 9780898716764 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022289322 |
| oclc_num | 698910785 |
| open_access_boolean | |
| owner | DE-188 DE-11 DE-29T DE-20 |
| owner_facet | DE-188 DE-11 DE-29T DE-20 |
| physical | XIII, 128 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | SIAM |
| record_format | marc |
| spellingShingle | Ipsen, Ilse C. F. Numerical matrix analysis linear systems and least squares Matrizenanalysis (DE-588)4227735-8 gnd |
| subject_GND | (DE-588)4227735-8 |
| title | Numerical matrix analysis linear systems and least squares |
| title_auth | Numerical matrix analysis linear systems and least squares |
| title_exact_search | Numerical matrix analysis linear systems and least squares |
| title_full | Numerical matrix analysis linear systems and least squares Ilse C. F. Ipsen |
| title_fullStr | Numerical matrix analysis linear systems and least squares Ilse C. F. Ipsen |
| title_full_unstemmed | Numerical matrix analysis linear systems and least squares Ilse C. F. Ipsen |
| title_short | Numerical matrix analysis |
| title_sort | numerical matrix analysis linear systems and least squares |
| title_sub | linear systems and least squares |
| topic | Matrizenanalysis (DE-588)4227735-8 gnd |
| topic_facet | Matrizenanalysis |
| url | http://www.gbv.de/dms/bowker/toc/9780898716764.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022289322&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ipsenilsecf numericalmatrixanalysislinearsystemsandleastsquares |