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Article: Numerical behaviour of multigrid methods for symmetric Sinc-Galerkin systems
Title | Numerical behaviour of multigrid methods for symmetric Sinc-Galerkin systems |
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Authors | |
Keywords | Toeplitz systems Multigrid Preconditioning Sinc-Galerkin methods |
Issue Date | 2005 |
Citation | Numerical Linear Algebra with Applications, 2005, v. 12, n. 2-3, p. 261-269 How to Cite? |
Abstract | The symmetric Sinc-Galerkin method developed by Lund (Math. Comput. 1986; 47:571-588), when applied to second-order self-adjoint boundary value problems on d dimensional rectangular domains, gives rise to an N × N positive definite coefficient matrix which can be viewed as the sum of d Kronecker products among d - 1 real diagonal matrices and one symmetric Toeplitz-plus-diagonal matrix. Thus, the resulting coefficient matrix has a strong structure so that it can be advantageously used in solving the discrete system. The main contribution of this paper is to present and analyse a multigrid method for these Sinc-Galerkin systems. In particular, we show by numerical examples that the solution of a discrete symmetric Sinc-Galerkin system can be obtained in an optimal way only using O(N log N) arithmetic operations. Numerical examples concerning one- and two-dimensional problems show that the multigrid method is practical and efficient for solving the above symmetric Sinc-Galerkin linear system. Copyright © 2004 John Wiley & Sons, Ltd. |
Persistent Identifier | http://hdl.handle.net/10722/276750 |
ISSN | 2023 Impact Factor: 1.8 2023 SCImago Journal Rankings: 0.932 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Serra-Capizzano, Stefano | - |
dc.contributor.author | Tablino-Possio, Cristina | - |
dc.date.accessioned | 2019-09-18T08:34:33Z | - |
dc.date.available | 2019-09-18T08:34:33Z | - |
dc.date.issued | 2005 | - |
dc.identifier.citation | Numerical Linear Algebra with Applications, 2005, v. 12, n. 2-3, p. 261-269 | - |
dc.identifier.issn | 1070-5325 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276750 | - |
dc.description.abstract | The symmetric Sinc-Galerkin method developed by Lund (Math. Comput. 1986; 47:571-588), when applied to second-order self-adjoint boundary value problems on d dimensional rectangular domains, gives rise to an N × N positive definite coefficient matrix which can be viewed as the sum of d Kronecker products among d - 1 real diagonal matrices and one symmetric Toeplitz-plus-diagonal matrix. Thus, the resulting coefficient matrix has a strong structure so that it can be advantageously used in solving the discrete system. The main contribution of this paper is to present and analyse a multigrid method for these Sinc-Galerkin systems. In particular, we show by numerical examples that the solution of a discrete symmetric Sinc-Galerkin system can be obtained in an optimal way only using O(N log N) arithmetic operations. Numerical examples concerning one- and two-dimensional problems show that the multigrid method is practical and efficient for solving the above symmetric Sinc-Galerkin linear system. Copyright © 2004 John Wiley & Sons, Ltd. | - |
dc.language | eng | - |
dc.relation.ispartof | Numerical Linear Algebra with Applications | - |
dc.subject | Toeplitz systems | - |
dc.subject | Multigrid | - |
dc.subject | Preconditioning | - |
dc.subject | Sinc-Galerkin methods | - |
dc.title | Numerical behaviour of multigrid methods for symmetric Sinc-Galerkin systems | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1002/nla.418 | - |
dc.identifier.scopus | eid_2-s2.0-20744435750 | - |
dc.identifier.volume | 12 | - |
dc.identifier.issue | 2-3 | - |
dc.identifier.spage | 261 | - |
dc.identifier.epage | 269 | - |
dc.identifier.isi | WOS:000228112200020 | - |
dc.identifier.issnl | 1070-5325 | - |