Developments and applications of block toeplitz iterative solvers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Beijing [u.a.]
Science Press [u.a.]
2002
|
| Schriftenreihe: | Combinatorics and computer science
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 218 S. |
| ISBN: | 7030107195 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Titel: Developments and applications of Block Toeplitz iterative solvers
Autor: Jin, Xiao-Qing
Jahr: 2002
CONTENTS
Preface ............................................................ix
Chapter 1 Introduction.........................................1
1.1 Background ................................................ 1
1.2 Circulant preconditioners..................................14
1.3 Non-circulant preconditioners ............................. 18
Chapter 2 Block Circulant Preconditioners .................24
2.1 Operators for block matrices .............................. 25
2.2 Operation cost for preconditioned system..................36
2.3 Convergence rate.......................................... 40
2.4 Invertibility of r^(Tmn) and s^F(Tmn) .................. 49
2.5 Numerical results ......................................... 53
Chapter 3 BCCB Preconditioners from Kernels ............56
3.1 Introduction .............................................. 56
3.2 Preconditioners from kernels .............................. 58
3.3 Clustering properties ......................................63
Chapter 4 Fast Algorithm for Tensor Structure ............66
4.1 Construction of preconditioner ............................ 66
4.2 Fast algorithm ............................................ 68
4.3 Inverse heat problem ...................................... 70
4.4 Numerical results ......................................... 72
Chapter 5 Block Toeplitz LS Problems ......................76
5.1 Introduction .............................................. 76
5.2 Construction of preconditioner ............................ 78
5.3 Spectrum of preconditioned matrix ........................81
5.4 Convergence rate and operation cost ...................... 84
Chapter 6 Block {o }-Circulant Preconditioners ............86
6.1 Spectral analysis .......................................... 86
6.2 Construction of preconditioner ............................ 91
6.3 Clustering of eigenvalues .................................. 94
6.4 Numerical results ........................................ 100
Chapter 7 Non-Circulant Block Preconditioners ..........102
7.1 Block band Toeplitz preconditioners...................... 102
yjjj Contents
7.2 Preconditioners based on fast transforms ................. 107
Chapter 8 Multigrid Block Toeplitz Solvers................110
8.1 Introduction ............................................. HO
8.2 Convergence rate of TGM ................................ 112
8.3 Convergence result for full MGM ......................... 117
8.4 Numerical results ........................................ 121
Chapter 9 Applications in Second-Order PDEs ............124
9.1 Applications to elliptic problems ......................... 124
9.2 Applications to hyperbolic problems......................127
9.3 Extension to parabolic equations ......................... 139
9.4 Numerical results ........................................ 142
9.5 3-dimensional problems .................................. 145
Chapter 10 Applications in First-Order PDEs .............150
10.1 Discretized system and GMRES method ................ 151
10.2 Construction of preconditioner .......................... 155
10.3 Convergence rate ....................................... 156
10.4 Spectral analysis ........................................ 158
10.5 Asymptotic properties .................................. 165
10.6 Convergence results and numerical tests................. 168
Chapter 11 Applications in ODEs and DAEs ..............180
11.1 BVMs and their matrix forms........................... 180
11.2 Construction of preconditioner .......................... 184
11.3 Convergence rate and operation cost .................... 187
11.4 Algorithm for DAEs .................................... 189
11.5 Numerical results ....................................... 192
Chapter 12 Applications in Image Processing .............198
12.1 Introduction ............................................ 198
12.2 Regularized PCGLS method ............................ 200
12.3 Numerical results ....................................... 202
Bibliography .................................................... 207
Index ............................................................ 216
|
| any_adam_object | 1 |
| author | Jin, Xiao-Qing |
| author_GND | (DE-588)13372817X |
| author_facet | Jin, Xiao-Qing |
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| author_sort | Jin, Xiao-Qing |
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| bvnumber | BV023836631 |
| ctrlnum | (OCoLC)890334473 (DE-599)BVBBV023836631 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:37:43Z |
| institution | BVB |
| isbn | 7030107195 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017478752 |
| oclc_num | 890334473 |
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| physical | XIII, 218 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Science Press [u.a.] |
| record_format | marc |
| series | Combinatorics and computer science |
| series2 | Combinatorics and computer science |
| spelling | Jin, Xiao-Qing Verfasser (DE-588)13372817X aut Developments and applications of block toeplitz iterative solvers by Xiao-Qing Jin Beijing [u.a.] Science Press [u.a.] 2002 XIII, 218 S. txt rdacontent n rdamedia nc rdacarrier Combinatorics and computer science 2 Iteration (DE-588)4123457-1 gnd rswk-swf Toeplitz-Matrix (DE-588)4185611-9 gnd rswk-swf Toeplitz-Matrix (DE-588)4185611-9 s Iteration (DE-588)4123457-1 s DE-604 Combinatorics and computer science 2 (DE-604)BV023818257 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478752&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jin, Xiao-Qing Developments and applications of block toeplitz iterative solvers Combinatorics and computer science Iteration (DE-588)4123457-1 gnd Toeplitz-Matrix (DE-588)4185611-9 gnd |
| subject_GND | (DE-588)4123457-1 (DE-588)4185611-9 |
| title | Developments and applications of block toeplitz iterative solvers |
| title_auth | Developments and applications of block toeplitz iterative solvers |
| title_exact_search | Developments and applications of block toeplitz iterative solvers |
| title_full | Developments and applications of block toeplitz iterative solvers by Xiao-Qing Jin |
| title_fullStr | Developments and applications of block toeplitz iterative solvers by Xiao-Qing Jin |
| title_full_unstemmed | Developments and applications of block toeplitz iterative solvers by Xiao-Qing Jin |
| title_short | Developments and applications of block toeplitz iterative solvers |
| title_sort | developments and applications of block toeplitz iterative solvers |
| topic | Iteration (DE-588)4123457-1 gnd Toeplitz-Matrix (DE-588)4185611-9 gnd |
| topic_facet | Iteration Toeplitz-Matrix |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478752&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023818257 |
| work_keys_str_mv | AT jinxiaoqing developmentsandapplicationsofblocktoeplitziterativesolvers |