File Download
There are no files associated with this item.
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1137/080720280
- Scopus: eid_2-s2.0-77953847485
- WOS: WOS:000278576300016
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: Approximate inverse circulant-plus-diagonal preconditioners for toeplitz-plus-diagonal matrices
Title | Approximate inverse circulant-plus-diagonal preconditioners for toeplitz-plus-diagonal matrices |
---|---|
Authors | |
Keywords | Convergence analysis Toeplitz-plus-diagonal matrices Approximate inverse Circulant matrices |
Issue Date | 2010 |
Citation | SIAM Journal on Scientific Computing, 2010, v. 32, n. 3, p. 1442-1464 How to Cite? |
Abstract | We consider the solutions of Hermitian positive definite Toeplitz-plus-diagonal systems (T +D)x = b, where T is a Toeplitz matrix and D is diagonal and positive. However, unlike the case of Toeplitz systems, no fast direct solvers have been developed for solving them. In this paper, we employ the preconditioned conjugate gradient method with approximate inverse circulant-plusdiagonal preconditioners to solving such systems. The proposed preconditioner can be constructed and implemented efficiently using fast Fourier transforms. We show that if the entries of T decay away exponentially from the main diagonals, the preconditioned conjugate gradient method applied to the preconditioned system converges very quickly. Numerical examples including spatial regularization for image deconvolution application are given to illustrate the effectiveness of the proposed preconditioner. © 2010 Society for Industrial and Applied Mathematics. |
Persistent Identifier | http://hdl.handle.net/10722/276864 |
ISSN | 2023 Impact Factor: 3.0 2023 SCImago Journal Rankings: 1.803 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Pan, Jianyu | - |
dc.date.accessioned | 2019-09-18T08:34:53Z | - |
dc.date.available | 2019-09-18T08:34:53Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | SIAM Journal on Scientific Computing, 2010, v. 32, n. 3, p. 1442-1464 | - |
dc.identifier.issn | 1064-8275 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276864 | - |
dc.description.abstract | We consider the solutions of Hermitian positive definite Toeplitz-plus-diagonal systems (T +D)x = b, where T is a Toeplitz matrix and D is diagonal and positive. However, unlike the case of Toeplitz systems, no fast direct solvers have been developed for solving them. In this paper, we employ the preconditioned conjugate gradient method with approximate inverse circulant-plusdiagonal preconditioners to solving such systems. The proposed preconditioner can be constructed and implemented efficiently using fast Fourier transforms. We show that if the entries of T decay away exponentially from the main diagonals, the preconditioned conjugate gradient method applied to the preconditioned system converges very quickly. Numerical examples including spatial regularization for image deconvolution application are given to illustrate the effectiveness of the proposed preconditioner. © 2010 Society for Industrial and Applied Mathematics. | - |
dc.language | eng | - |
dc.relation.ispartof | SIAM Journal on Scientific Computing | - |
dc.subject | Convergence analysis | - |
dc.subject | Toeplitz-plus-diagonal matrices | - |
dc.subject | Approximate inverse | - |
dc.subject | Circulant matrices | - |
dc.title | Approximate inverse circulant-plus-diagonal preconditioners for toeplitz-plus-diagonal matrices | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/080720280 | - |
dc.identifier.scopus | eid_2-s2.0-77953847485 | - |
dc.identifier.volume | 32 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 1442 | - |
dc.identifier.epage | 1464 | - |
dc.identifier.isi | WOS:000278576300016 | - |
dc.identifier.issnl | 1064-8275 | - |