Computational matrix analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
SIAM, Soc. for Indust. and Appl. Math.
2012
|
| Schriftenreihe: | Other titles in applied mathematics
125 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 154 S. |
| ISBN: | 9781611972207 |
Internformat
MARC
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| 020 | |a 9781611972207 |9 978-1-611972-20-7 | ||
| 024 | 3 | |a 9781611972207 | |
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| 100 | 1 | |a Laub, Alan J. |d 1948- |e Verfasser |0 (DE-588)115244735 |4 aut | |
| 245 | 1 | 0 | |a Computational matrix analysis |c Alan J. Laub |
| 264 | 1 | |a Philadelphia |b SIAM, Soc. for Indust. and Appl. Math. |c 2012 | |
| 300 | |a XIII, 154 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Other titles in applied mathematics |v 125 | |
| 830 | 0 | |a Other titles in applied mathematics |v 125 |w (DE-604)BV023088396 |9 125 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025419131&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025419131 | ||
Datensatz im Suchindex
| _version_ | 1804149676776095744 |
|---|---|
| adam_text | Titel: Computational matrix analysis
Autor: Laub, Alan J
Jahr: 2012
Contents
Preface ix
Listings xiii
Notation and Acronyms xv
1 Introduction and preliminaries 1
1.1 Matrix equations .......................... 2
1.2 Algebraic Riccati equations..................... 3
1.2.1 Nonsymmetric equations ............... 3
1.2.2 Equations associated with M-matrices........ 3
1.2.3 Continuous-time equations.............. 5
1.2.4 Discrete-time equations................ 6
1.3 Unilateral quadratic matrix equations............... 8
1.4 Useful concepts and definitions................... 9
1.4.1 Invariant and deflating subspaces........... 9
1.4.2 Some definitions from control theory......... 11
1.4.3 Matrix polynomials.................. 12
1.4.4 Eigenvalue transformations.............. 14
1.4.5 Splitting properties .................. 20
1.5 Hamiltonian and symplectic matrices............... 22
1.6 Algorithmic issues.......................... 26
1.6.1 Convergence speed................... 26
1.6.2 Cost of elementary matrix Operations........ 28
1.6.3 Conditioning and numerical stability......... 29
1.7 Available Software.......................... 30
1.8 Additional notes and further reading............... 31
2 Theoretical analysis 33
2.1 Invariant subspaces and algebraic Riccati equations....... 33
2.1.1 Nonsymmetric equations ............... 33
2.1.2 Equations associated with M-matrices........ 37
2.1.3 Continuous-time equations.............. 39
2.1.4 Discrete-time equations................ 40
vi Contents
2.2 Extremal Solutions ......................... 41
2.2.1 Equations associated with M-matrices........ 42
2.2.2 Continuous-time equations.............. 46
2.2.3 Discrete-time equations................ 49
2.3 Critical Solutions .......................... 50
2.4 Shift techniques........................... 52
2.4.1 Equations associated with M-matrices........ 54
2.4.2 Continuous-time equations.............. 57
2.5 Transformations between discrete- and continuous-time..... 61
2.6 Unilateral quadratic matrix equations............... 62
2.7 Transforming an algebraic Riccati equation to a UQME..... 67
2.7.1 Simple transformation................. 68
2.7.2 UL-based transformation............... 70
2.7.3 Reduction to a UQME of lower size......... 73
2.8 Perturbation results......................... 75
2.8.1 Algebraic Riccati equations.............. 76
2.8.2 UQMEs......................... 80
2.9 Additional notes and further reading............... 81
3 Classical algorithms 83
3.1 Linear matrix equations....................... 83
3.1.1 Sylvester, Lyapunov, and Stein equations...... 83
3.1.2 Generalized equations................. 87
3.2 Invariant subspaces methods.................... 87
3.2.1 Balancing technique.................. 92
3.3 Newton s method.......................... 92
3.3.1 Continuous-time equations.............. 93
3.3.2 Equations associated with M-matrices........ 98
3.3.3 Other algebraic Riccati equations........... 101
3.3.4 Iterative refinement and defect correction...... 102
3.4 Functional iterations ........................ 103
3.5 Matrix sign function method.................... 105
3.5.1 Continuous-time equations.............. 105
3.5.2 Computing the matrix sign function......... 107
3.5.3 Other algebraic Riccati equations........... 109
3.6 Numerical experiments....................... 111
3.6.1 Continuous-time equations.............. 111
3.6.2 Equations associated with M-matrices........ 114
3.7 Additional notes and further reading............... 118
4 Structured invariant subspace methods 121
4.1 Elementary matrices ........................ 122
4.2 Hamiltonian Condensed and special forms............. 125
4.2.1 The PVL form..................... 126
4.2.2 URV Decomposition.................. 128
4.2.3 Other Condensed forms ................ 131
Contents vii
4.3 Hamiltonian QR algorithm..................... 131
4.3.1 The Hamiltonian/symplectic QR step........ 133
4.4 Computation of the eigenvalues of a Hamiltonian matrix .... 135
4.5 The URV algorithms........................ 136
4.6 The multishift algorithm...................... 140
4.7 Additional notes and further reading............... 142
5 Doubling algorithms 145
5.1 Structured doubling algorithm................... 146
5.1.1 SDA-I.......................... 147
5.1.2 SDA-II......................... 151
5.1.3 QR-based doubling algorithm............. 153
5.2 Cyclic reduction........................... 155
5.2.1 Convergence properties................ 158
5.2.2 Applicability...................... 161
5.2.3 Interplay with SDAs.................. 167
5.3 Solving algebraic Riccati equations................ 168
5.3.1 Equations associated with M-matrices........ 168
5.3.2 Continuous-time equations.............. 179
5.3.3 Discrete-time equations................ 184
5.4 Acceleration techniques....................... 188
5.5 Numerical experiments....................... 190
5.5.1 Continuous-time equations.............. 190
5.5.2 Equations associated with M-matrices........ 191
5.6 Additional notes and further reading............... 192
6 Algorithms for large-scale problems 195
6.1 Linear matrix equations with large and sparse coefficients .... 196
6.1.1 The ADI iteration................... 196
6.1.2 Cholesky factor ADI.................. 198
6.1.3 Krylov subspace methods............... 201
6.2 Continuous- and discrete-time Riccati equations......... 204
6.3 Additional notes and further reading............... 206
A Basic properties 209
A.l Norms and spectral radius..................... 209
A.2 Matrix factorizations and decompositions............. 211
A.3 Krylov subspaces.......................... 213
A.4 Properties of Kronecker product.................. 214
A.5 Nonnegative matrices and M-matrices............... 215
A.6 Matrix funetions and Laurent power series............ 216
viii Contents
A.7 Frechet derivative and its properties................217
A.8 Elementary matrices ........................218
Bibliography 221
Index 245
|
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| id | DE-604.BV040591198 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:26:49Z |
| institution | BVB |
| isbn | 9781611972207 |
| language | English |
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| physical | XIII, 154 S. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | SIAM, Soc. for Indust. and Appl. Math. |
| record_format | marc |
| series | Other titles in applied mathematics |
| series2 | Other titles in applied mathematics |
| spelling | Laub, Alan J. 1948- Verfasser (DE-588)115244735 aut Computational matrix analysis Alan J. Laub Philadelphia SIAM, Soc. for Indust. and Appl. Math. 2012 XIII, 154 S. txt rdacontent n rdamedia nc rdacarrier Other titles in applied mathematics 125 Other titles in applied mathematics 125 (DE-604)BV023088396 125 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025419131&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Laub, Alan J. 1948- Computational matrix analysis Other titles in applied mathematics |
| title | Computational matrix analysis |
| title_auth | Computational matrix analysis |
| title_exact_search | Computational matrix analysis |
| title_full | Computational matrix analysis Alan J. Laub |
| title_fullStr | Computational matrix analysis Alan J. Laub |
| title_full_unstemmed | Computational matrix analysis Alan J. Laub |
| title_short | Computational matrix analysis |
| title_sort | computational matrix analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025419131&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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