Holdings: Developments and applications of block toeplitz iterative solvers

Developments and applications of block toeplitz iterative solvers:

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Bibliographic Details
Main Author:	Jin, Xiao-Qing (Author)
Format:	Book
Language:	English
Published:	Beijing [u.a.] Science Press [u.a.] 2002
Series:	Combinatorics and computer science 2
Subjects:	Iteration Toeplitz-Matrix
Online Access:	Inhaltsverzeichnis
Physical Description:	XIII, 218 S.
ISBN:	7030107195

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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
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author	Jin, Xiao-Qing
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dewey-tens	510 - Mathematics
discipline	Mathematik
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illustrated	Not Illustrated
indexdate	2024-07-09T21:37:43Z
institution	BVB
isbn	7030107195
language	English
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physical	XIII, 218 S.
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publisher	Science Press [u.a.]
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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

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