File Download
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1137/S0895479803428230
- Scopus: eid_2-s2.0-54849429866
- WOS: WOS:000253016700004
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: Block diagonal and schur complement preconditioners for block-toeplitz systems with small size blocks
Title | Block diagonal and schur complement preconditioners for block-toeplitz systems with small size blocks |
---|---|
Authors | |
Keywords | Block diagonal Block-toeplitz matrix Preconditioners Recursion Schur complement |
Issue Date | 2007 |
Publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/simax.php |
Citation | Siam Journal On Matrix Analysis And Applications, 2007, v. 29 n. 4, p. 1101-1119 How to Cite? |
Abstract | In this paper we consider the solution of Hermitian positive definite block-Toeplitz systems with small size blocks. We propose and study block diagonal and Schur complement preconditioners for such block-Toeplitz matrices. We show that for some block-Toeplitz matrices, the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers where this fixed number depends only on the size of the block. Hence, conjugate gradient type methods, when applied to solving these preconditioned block-Toeplitz systems with small size blocks, converge very fast. Recursive computation of such block diagonal and Schur complement preconditioners is considered by using the nice matrix representation of the inverse of a block-Toeplitz matrix. Applications to block-Toeplitz systems arising from least squares filtering problems and queueing networks are presented. Numerical examples are given to demonstrate the effectiveness of the proposed method. © 2007 Society for Industrial and Applied Mathematics. |
Persistent Identifier | http://hdl.handle.net/10722/75407 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 1.042 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Ching, WK | en_HK |
dc.contributor.author | Ng, MK | en_HK |
dc.contributor.author | Wen, YW | en_HK |
dc.date.accessioned | 2010-09-06T07:10:49Z | - |
dc.date.available | 2010-09-06T07:10:49Z | - |
dc.date.issued | 2007 | en_HK |
dc.identifier.citation | Siam Journal On Matrix Analysis And Applications, 2007, v. 29 n. 4, p. 1101-1119 | en_HK |
dc.identifier.issn | 0895-4798 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/75407 | - |
dc.description.abstract | In this paper we consider the solution of Hermitian positive definite block-Toeplitz systems with small size blocks. We propose and study block diagonal and Schur complement preconditioners for such block-Toeplitz matrices. We show that for some block-Toeplitz matrices, the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers where this fixed number depends only on the size of the block. Hence, conjugate gradient type methods, when applied to solving these preconditioned block-Toeplitz systems with small size blocks, converge very fast. Recursive computation of such block diagonal and Schur complement preconditioners is considered by using the nice matrix representation of the inverse of a block-Toeplitz matrix. Applications to block-Toeplitz systems arising from least squares filtering problems and queueing networks are presented. Numerical examples are given to demonstrate the effectiveness of the proposed method. © 2007 Society for Industrial and Applied Mathematics. | en_HK |
dc.language | eng | en_HK |
dc.publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/simax.php | - |
dc.relation.ispartof | SIAM Journal on Matrix Analysis and Applications | en_HK |
dc.rights | © 2007 Society for Industrial and Applied Mathematics. First Published in SIAM Journal on Matrix Analysis and Applications in volume 29, issue 4, published by the Society for Industrial and Applied Mathematics (SIAM). | - |
dc.subject | Block diagonal | en_HK |
dc.subject | Block-toeplitz matrix | en_HK |
dc.subject | Preconditioners | en_HK |
dc.subject | Recursion | en_HK |
dc.subject | Schur complement | en_HK |
dc.title | Block diagonal and schur complement preconditioners for block-toeplitz systems with small size blocks | en_HK |
dc.type | Article | en_HK |
dc.identifier.email | Ching, WK:wching@hku.hk | en_HK |
dc.identifier.authority | Ching, WK=rp00679 | en_HK |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1137/S0895479803428230 | en_HK |
dc.identifier.scopus | eid_2-s2.0-54849429866 | en_HK |
dc.identifier.hkuros | 141945 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-54849429866&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 29 | en_HK |
dc.identifier.issue | 4 | en_HK |
dc.identifier.spage | 1101 | en_HK |
dc.identifier.epage | 1119 | en_HK |
dc.identifier.eissn | 1095-7162 | - |
dc.identifier.isi | WOS:000253016700004 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Ching, WK=13310265500 | en_HK |
dc.identifier.scopusauthorid | Ng, MK=34571761900 | en_HK |
dc.identifier.scopusauthorid | Wen, YW=7401777008 | en_HK |
dc.identifier.issnl | 0895-4798 | - |