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Article: Strang-type preconditioners for systems of LMF-based ODE codes
Title | Strang-type preconditioners for systems of LMF-based ODE codes |
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Authors | |
Issue Date | 2001 |
Citation | IMA Journal of Numerical Analysis, 2001, v. 21, n. 2, p. 451-462 How to Cite? |
Abstract | We consider the solution of ordinary differential equations (ODEs) using boundary value methods. These methods require the solution of one or more unsymmetric, large and sparse linear systems. The GMRES method with the Strang-type block-circulant preconditioner is proposed for solving these linear systems. We show that if an Ak1,k2-stable boundary value method is used for an m-by-m system of ODEs, then our preconditioners are invertible and all the eigenvalues of the preconditioned systems are 1 except for at most 2m(k1 + k2) outliers. It follows that when the GMRES method is applied to solving the preconditioned systems, the method will converge in at most 2m(k1 + k2) + 1 iterations. Numerical results are given to illustrate the effectiveness of our methods. |
Persistent Identifier | http://hdl.handle.net/10722/276725 |
ISSN | 2023 Impact Factor: 2.3 2023 SCImago Journal Rankings: 1.861 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chan, Raymond H. | - |
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Jin, Xiao Qing | - |
dc.date.accessioned | 2019-09-18T08:34:28Z | - |
dc.date.available | 2019-09-18T08:34:28Z | - |
dc.date.issued | 2001 | - |
dc.identifier.citation | IMA Journal of Numerical Analysis, 2001, v. 21, n. 2, p. 451-462 | - |
dc.identifier.issn | 0272-4979 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276725 | - |
dc.description.abstract | We consider the solution of ordinary differential equations (ODEs) using boundary value methods. These methods require the solution of one or more unsymmetric, large and sparse linear systems. The GMRES method with the Strang-type block-circulant preconditioner is proposed for solving these linear systems. We show that if an Ak1,k2-stable boundary value method is used for an m-by-m system of ODEs, then our preconditioners are invertible and all the eigenvalues of the preconditioned systems are 1 except for at most 2m(k1 + k2) outliers. It follows that when the GMRES method is applied to solving the preconditioned systems, the method will converge in at most 2m(k1 + k2) + 1 iterations. Numerical results are given to illustrate the effectiveness of our methods. | - |
dc.language | eng | - |
dc.relation.ispartof | IMA Journal of Numerical Analysis | - |
dc.title | Strang-type preconditioners for systems of LMF-based ODE codes | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1093/imanum/21.2.451 | - |
dc.identifier.scopus | eid_2-s2.0-0035531729 | - |
dc.identifier.volume | 21 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 451 | - |
dc.identifier.epage | 462 | - |
dc.identifier.isi | WOS:000168263700001 | - |
dc.identifier.issnl | 0272-4979 | - |