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Article: Constraint preconditioners for symmetric indefinite matrices
Title | Constraint preconditioners for symmetric indefinite matrices |
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Authors | |
Keywords | Symmetric indefinite systems Constraint preconditioners |
Issue Date | 2009 |
Citation | SIAM Journal on Matrix Analysis and Applications, 2009, v. 31, n. 2, p. 410-433 How to Cite? |
Abstract | We study the eigenvalue bounds of block two-by-two nonsingular and symmetric indefinite matrices whose (1, 1) block is symmetric positive d efinite and Schur complement with respect to its (2, 2) block is symmetric indefinite. A constraint preconditioner for this matrix is constructed by simply replacing the (1, 1) block by a symmetric and positive definite approximation, and the spectral properties of the preconditioned matrix are discussed. Numerical results show that, for a suitably chosen (1, 1) block-matrix, this constraint preconditioner outperforms the block-diagonal and the block-tridiagonal ones in iteration step and computing time when they are used to accelerate the GMRES method for solving these block two-by-two symmetric positive indefinite linear systems. The new results extend the existing ones about block two-by-two matrices of symmetric negative semidefinite (2, 2) blocks to those of general symmetric (2, 2) blocks. © 2009 Society for Industrial and Applied Mathematics. |
Persistent Identifier | http://hdl.handle.net/10722/276850 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 1.042 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bal, Zhong Zhi | - |
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Wang, Zeng Qi | - |
dc.date.accessioned | 2019-09-18T08:34:51Z | - |
dc.date.available | 2019-09-18T08:34:51Z | - |
dc.date.issued | 2009 | - |
dc.identifier.citation | SIAM Journal on Matrix Analysis and Applications, 2009, v. 31, n. 2, p. 410-433 | - |
dc.identifier.issn | 0895-4798 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276850 | - |
dc.description.abstract | We study the eigenvalue bounds of block two-by-two nonsingular and symmetric indefinite matrices whose (1, 1) block is symmetric positive d efinite and Schur complement with respect to its (2, 2) block is symmetric indefinite. A constraint preconditioner for this matrix is constructed by simply replacing the (1, 1) block by a symmetric and positive definite approximation, and the spectral properties of the preconditioned matrix are discussed. Numerical results show that, for a suitably chosen (1, 1) block-matrix, this constraint preconditioner outperforms the block-diagonal and the block-tridiagonal ones in iteration step and computing time when they are used to accelerate the GMRES method for solving these block two-by-two symmetric positive indefinite linear systems. The new results extend the existing ones about block two-by-two matrices of symmetric negative semidefinite (2, 2) blocks to those of general symmetric (2, 2) blocks. © 2009 Society for Industrial and Applied Mathematics. | - |
dc.language | eng | - |
dc.relation.ispartof | SIAM Journal on Matrix Analysis and Applications | - |
dc.subject | Symmetric indefinite systems | - |
dc.subject | Constraint preconditioners | - |
dc.title | Constraint preconditioners for symmetric indefinite matrices | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/080720243 | - |
dc.identifier.scopus | eid_2-s2.0-72449132302 | - |
dc.identifier.volume | 31 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 410 | - |
dc.identifier.epage | 433 | - |
dc.identifier.eissn | 1095-7162 | - |
dc.identifier.isi | WOS:000267745500011 | - |
dc.identifier.issnl | 0895-4798 | - |