MN-PGSOR Method for Solving Nonlinear Systems with Block Two-by-Two Complex Symmetric Jacobian Matrices
For solving the large sparse linear systems with 2×2 block structure, the generalized successive overrelaxation (GSOR) iteration method is an efficient iteration method. Based on the GSOR method, the PGSOR method introduces a preconditioned matrix with a new parameter for the coefficient matrix whic...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/4393353 |
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| author | Yu-Ye Feng Qing-Biao Wu |
| author_facet | Yu-Ye Feng Qing-Biao Wu |
| author_sort | Yu-Ye Feng |
| collection | DOAJ |
| description | For solving the large sparse linear systems with 2×2 block structure, the generalized successive overrelaxation (GSOR) iteration method is an efficient iteration method. Based on the GSOR method, the PGSOR method introduces a preconditioned matrix with a new parameter for the coefficient matrix which can enhance the efficiency. To solve the nonlinear systems in which the Jacobian matrices are complex and symmetric with the block two-by-two form, we try to use the PGSOR method as an inner iteration, with the help of the modified Newton method as an efficient outer iteration method. This new method is called the modified Newton-PGSOR (MN-PGSOR) method. Local convergence properties of the MN-PGSOR are analyzed under the Hölder condition. Finally, we give the comparison of our new method with some previous methods in the numerical results. The MN-PGSOR method is superior in both iteration steps and computing time. |
| format | Article |
| id | doaj-art-fe99e8a5be964d949edbefdaffcacfff |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-fe99e8a5be964d949edbefdaffcacfff2025-08-20T03:25:46ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/43933534393353MN-PGSOR Method for Solving Nonlinear Systems with Block Two-by-Two Complex Symmetric Jacobian MatricesYu-Ye Feng0Qing-Biao Wu1School of Mathematical Science, Zhejiang University, Zhejiang, Hangzhou 310027, ChinaSchool of Mathematical Science, Zhejiang University, Zhejiang, Hangzhou 310027, ChinaFor solving the large sparse linear systems with 2×2 block structure, the generalized successive overrelaxation (GSOR) iteration method is an efficient iteration method. Based on the GSOR method, the PGSOR method introduces a preconditioned matrix with a new parameter for the coefficient matrix which can enhance the efficiency. To solve the nonlinear systems in which the Jacobian matrices are complex and symmetric with the block two-by-two form, we try to use the PGSOR method as an inner iteration, with the help of the modified Newton method as an efficient outer iteration method. This new method is called the modified Newton-PGSOR (MN-PGSOR) method. Local convergence properties of the MN-PGSOR are analyzed under the Hölder condition. Finally, we give the comparison of our new method with some previous methods in the numerical results. The MN-PGSOR method is superior in both iteration steps and computing time.http://dx.doi.org/10.1155/2021/4393353 |
| spellingShingle | Yu-Ye Feng Qing-Biao Wu MN-PGSOR Method for Solving Nonlinear Systems with Block Two-by-Two Complex Symmetric Jacobian Matrices Journal of Mathematics |
| title | MN-PGSOR Method for Solving Nonlinear Systems with Block Two-by-Two Complex Symmetric Jacobian Matrices |
| title_full | MN-PGSOR Method for Solving Nonlinear Systems with Block Two-by-Two Complex Symmetric Jacobian Matrices |
| title_fullStr | MN-PGSOR Method for Solving Nonlinear Systems with Block Two-by-Two Complex Symmetric Jacobian Matrices |
| title_full_unstemmed | MN-PGSOR Method for Solving Nonlinear Systems with Block Two-by-Two Complex Symmetric Jacobian Matrices |
| title_short | MN-PGSOR Method for Solving Nonlinear Systems with Block Two-by-Two Complex Symmetric Jacobian Matrices |
| title_sort | mn pgsor method for solving nonlinear systems with block two by two complex symmetric jacobian matrices |
| url | http://dx.doi.org/10.1155/2021/4393353 |
| work_keys_str_mv | AT yuyefeng mnpgsormethodforsolvingnonlinearsystemswithblocktwobytwocomplexsymmetricjacobianmatrices AT qingbiaowu mnpgsormethodforsolvingnonlinearsystemswithblocktwobytwocomplexsymmetricjacobianmatrices |