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Article: The convergence rate of block preconditioned systems arising from LMF-based ode codes
Title | The convergence rate of block preconditioned systems arising from LMF-based ode codes |
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Authors | |
Keywords | Unsymmetric block (almost) Toeplitz linear systems Boundary value methods Rate of convergence Numerical solution of differential equations Implicit linear multistep formulas Circulant preconditioning |
Issue Date | 2001 |
Citation | BIT Numerical Mathematics, 2001, v. 41, n. 3, p. 433-450 How to Cite? |
Abstract | The solution of ordinary and partial differential equations using implicit linear multistep formulas (LMF) is considered. More precisely, boundary value methods (BVMs), a class of methods based on implicit formulas will be taken into account in this paper. These methods require the solution of large and sparse linear systems M̂x = b. Block-circulant preconditioners have been proposed to solve these linear system. By investigating the spectral condition number of M̂, we show that the conjugate gradient method, when applied to solving the normalized preconditioned system, converges in at most O(log s) steps, where the integration step size is O(1/s). Numerical results are given to illustrate the effectiveness of the analysis. |
Persistent Identifier | http://hdl.handle.net/10722/276478 |
ISSN | 2023 Impact Factor: 1.6 2023 SCImago Journal Rankings: 1.064 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bertaccini, Daniele | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:33:43Z | - |
dc.date.available | 2019-09-18T08:33:43Z | - |
dc.date.issued | 2001 | - |
dc.identifier.citation | BIT Numerical Mathematics, 2001, v. 41, n. 3, p. 433-450 | - |
dc.identifier.issn | 0006-3835 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276478 | - |
dc.description.abstract | The solution of ordinary and partial differential equations using implicit linear multistep formulas (LMF) is considered. More precisely, boundary value methods (BVMs), a class of methods based on implicit formulas will be taken into account in this paper. These methods require the solution of large and sparse linear systems M̂x = b. Block-circulant preconditioners have been proposed to solve these linear system. By investigating the spectral condition number of M̂, we show that the conjugate gradient method, when applied to solving the normalized preconditioned system, converges in at most O(log s) steps, where the integration step size is O(1/s). Numerical results are given to illustrate the effectiveness of the analysis. | - |
dc.language | eng | - |
dc.relation.ispartof | BIT Numerical Mathematics | - |
dc.subject | Unsymmetric block (almost) Toeplitz linear systems | - |
dc.subject | Boundary value methods | - |
dc.subject | Rate of convergence | - |
dc.subject | Numerical solution of differential equations | - |
dc.subject | Implicit linear multistep formulas | - |
dc.subject | Circulant preconditioning | - |
dc.title | The convergence rate of block preconditioned systems arising from LMF-based ode codes | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1023/A:1021906926616 | - |
dc.identifier.scopus | eid_2-s2.0-0043142566 | - |
dc.identifier.volume | 41 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 433 | - |
dc.identifier.epage | 450 | - |
dc.identifier.isi | WOS:000171285500001 | - |
dc.identifier.issnl | 0006-3835 | - |