The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2022 |
| Outros Autores: | , |
| Tipo de documento: | Artigo |
| Idioma: | por |
| Título da fonte: | Pesquisa e Ensino em Ciências Exatas e da Natureza |
| Texto Completo: | https://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECEN/article/view/1773 |
Resumo: | Here, m-order methods are developed that conserve the form of the first-order methods. The m-order methods have a higher rate of convergence than their first-order version. These m-order methods are subsequences of its precursor method, where some benefits of using vector and parallel processors can be explored. The numerical results obtained with vector implementations show computational advantages when compared to the first-order versions. |
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The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methodsThe m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methodsHere, m-order methods are developed that conserve the form of the first-order methods. The m-order methods have a higher rate of convergence than their first-order version. These m-order methods are subsequences of its precursor method, where some benefits of using vector and parallel processors can be explored. The numerical results obtained with vector implementations show computational advantages when compared to the first-order versions.Aqui, são desenvolvidos métodos de ordem m que conservam a forma dos métodos de primeiraordem. Métodos de ordem m têm uma taxa de convergência maior que sua versão de primeira ordem.Esses métodos de ordem m são subsequências de seu método precursor, onde alguns benefícios do usode processadores vetoriais e paralelos podem ser explorados. Os resultados numéricos obtidos com asimplementações vetoriais mostram vantagens computacionais quando comparadas as versões deprimeira ordem.Unidade Acadêmica de Ciências Exatas e da Natureza/CFP/UFCGUniversidade Federal FluminenseAlvarez, Gustavo BenitezLobão, Diomar CesarMenezes, Welton Alves de2022-03-28info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECEN/article/view/177310.29215/pecen.v6i0.1773Pesquisa e Ensino em Ciências Exatas e da Natureza; v. 6 (2022): Pesquisa e Ensino em Ciências Exatas e da Natureza; e17732526-823610.29215/pecen.v6i0reponame:Pesquisa e Ensino em Ciências Exatas e da Naturezainstname:Universidade Federal de Campina Grande (UFCG)instacron:UFCGporhttps://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECEN/article/view/1773/pdfhttps://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECEN/article/downloadSuppFile/1773/277https://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECEN/article/downloadSuppFile/1773/278/*ref*/Antuono M. and Colicchio G. (2016) Delayed Over-Relaxation for iterative methods. Journal of Computational Physics, 321: 892–907./*ref*/Apostol T.M. (1981) Mathematical analysis. Addilson-Wesley Publishing Company./*ref*/Bai Z.-Z. and Miao C.-Q. (2017) On local quadratic convergence of inexact simplified Jacobi–Davidson method. Linear Algebra and its Applications, 520: 215–241./*ref*/Bertaccini D. and Durastante F. (2018) Iterative methods and preconditioning for large and sparse linear systems with applications. Taylor & Francis Group./*ref*/Forsythe G.E. and Moler C.B. (1967) Computer solution of linear algebraic systems. Prentice-Hall, New Jersey./*ref*/Golub G.H. and Van Loan C. (2013) Matrix computations. The Johns Hopkins University Press, Baltimore, MD, 4th edition./*ref*/Golub G.H. and Varga R.S. (1961) Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods, Parts I and II. Numerische Mathematik, 3: 147–168./*ref*/Kahan W.M. (1958) Gauss–Seidel methods of solving large systems of linear equations. PhD thesis, University of Toronto, Toronto./*ref*/Kepner J. (2009) Parallel MATLAB for Multicore and Multinode Computers. Society for Industrial and Applied Mathematics, USA, 1st edition./*ref*/Kolodziej S.P., Aznaveh M., Bullock M., David J., Davis T.A., Henderson M., Hu Y. and Sandstrom R. (2019) The SuiteSparse Matrix Collection Website Interface. Journal of Open Source Software, 4(35): 1244–1248./*ref*/Kong Q., Jing Y.-F., Huang T.-Z. and An H.-B. (2019). Acceleration of the Scheduled Relaxation Jacobi method: Promising strategies for solving large, sparse linear systems. Journal of Computational Physics, 397:108862./*ref*/Mazza M., Manni C., Ratnani A., Serra-Capizzano S. and Speleers H. (2019) Isogeometric analysis for 2D and 3D curl–div problems: Spectral symbols and fast iterative solvers. Computer Methods in Applied Mechanics and Engineering, 344: 970–997.Direitos autorais 2022 Autor e Revista mantêm os direitos da publicaçãoinfo:eu-repo/semantics/openAccess2022-10-31T13:00:37Zoai:ojs.cfp.revistas.ufcg.edu.br:article/1773Revistahttps://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECENPUBhttps://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECEN/oai||cienciasexatasenatureza@gmail.com2526-82362526-8236opendoar:2022-10-31T13:00:37Pesquisa e Ensino em Ciências Exatas e da Natureza - Universidade Federal de Campina Grande (UFCG)false |
| dc.title.none.fl_str_mv |
The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods |
| title |
The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods |
| spellingShingle |
The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods Alvarez, Gustavo Benitez |
| title_short |
The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods |
| title_full |
The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods |
| title_fullStr |
The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods |
| title_full_unstemmed |
The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods |
| title_sort |
The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods |
| author |
Alvarez, Gustavo Benitez |
| author_facet |
Alvarez, Gustavo Benitez Lobão, Diomar Cesar Menezes, Welton Alves de |
| author_role |
author |
| author2 |
Lobão, Diomar Cesar Menezes, Welton Alves de |
| author2_role |
author author |
| dc.contributor.none.fl_str_mv |
Universidade Federal Fluminense |
| dc.contributor.author.fl_str_mv |
Alvarez, Gustavo Benitez Lobão, Diomar Cesar Menezes, Welton Alves de |
| description |
Here, m-order methods are developed that conserve the form of the first-order methods. The m-order methods have a higher rate of convergence than their first-order version. These m-order methods are subsequences of its precursor method, where some benefits of using vector and parallel processors can be explored. The numerical results obtained with vector implementations show computational advantages when compared to the first-order versions. |
| publishDate |
2022 |
| dc.date.none.fl_str_mv |
2022-03-28 |
| dc.type.none.fl_str_mv |
|
| dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
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article |
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publishedVersion |
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https://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECEN/article/view/1773 10.29215/pecen.v6i0.1773 |
| url |
https://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECEN/article/view/1773 |
| identifier_str_mv |
10.29215/pecen.v6i0.1773 |
| dc.language.iso.fl_str_mv |
por |
| language |
por |
| dc.relation.none.fl_str_mv |
https://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECEN/article/view/1773/pdf https://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECEN/article/downloadSuppFile/1773/277 https://cfp.revistas.ufcg.edu.br/cfp/index.php/RPECEN/article/downloadSuppFile/1773/278 /*ref*/Antuono M. and Colicchio G. (2016) Delayed Over-Relaxation for iterative methods. Journal of Computational Physics, 321: 892–907. /*ref*/Apostol T.M. (1981) Mathematical analysis. Addilson-Wesley Publishing Company. /*ref*/Bai Z.-Z. and Miao C.-Q. (2017) On local quadratic convergence of inexact simplified Jacobi–Davidson method. Linear Algebra and its Applications, 520: 215–241. /*ref*/Bertaccini D. and Durastante F. (2018) Iterative methods and preconditioning for large and sparse linear systems with applications. Taylor & Francis Group. /*ref*/Forsythe G.E. and Moler C.B. (1967) Computer solution of linear algebraic systems. Prentice-Hall, New Jersey. /*ref*/Golub G.H. and Van Loan C. (2013) Matrix computations. The Johns Hopkins University Press, Baltimore, MD, 4th edition. /*ref*/Golub G.H. and Varga R.S. (1961) Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods, Parts I and II. Numerische Mathematik, 3: 147–168. /*ref*/Kahan W.M. (1958) Gauss–Seidel methods of solving large systems of linear equations. PhD thesis, University of Toronto, Toronto. /*ref*/Kepner J. (2009) Parallel MATLAB for Multicore and Multinode Computers. Society for Industrial and Applied Mathematics, USA, 1st edition. /*ref*/Kolodziej S.P., Aznaveh M., Bullock M., David J., Davis T.A., Henderson M., Hu Y. and Sandstrom R. (2019) The SuiteSparse Matrix Collection Website Interface. Journal of Open Source Software, 4(35): 1244–1248. /*ref*/Kong Q., Jing Y.-F., Huang T.-Z. and An H.-B. (2019). Acceleration of the Scheduled Relaxation Jacobi method: Promising strategies for solving large, sparse linear systems. Journal of Computational Physics, 397:108862. /*ref*/Mazza M., Manni C., Ratnani A., Serra-Capizzano S. and Speleers H. (2019) Isogeometric analysis for 2D and 3D curl–div problems: Spectral symbols and fast iterative solvers. Computer Methods in Applied Mechanics and Engineering, 344: 970–997. |
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Direitos autorais 2022 Autor e Revista mantêm os direitos da publicação info:eu-repo/semantics/openAccess |
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Direitos autorais 2022 Autor e Revista mantêm os direitos da publicação |
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application/pdf |
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Unidade Acadêmica de Ciências Exatas e da Natureza/CFP/UFCG |
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Unidade Acadêmica de Ciências Exatas e da Natureza/CFP/UFCG |
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Pesquisa e Ensino em Ciências Exatas e da Natureza; v. 6 (2022): Pesquisa e Ensino em Ciências Exatas e da Natureza; e1773 2526-8236 10.29215/pecen.v6i0 reponame:Pesquisa e Ensino em Ciências Exatas e da Natureza instname:Universidade Federal de Campina Grande (UFCG) instacron:UFCG |
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