On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations
To avoid solving the complex systems, we first rewrite the complex-valued nonlinear system to real-valued form (C-to-R) equivalently. Then, based on separable property of the linear and the nonlinear terms, we present a C-to-R-based Picard iteration method and a nonlinear C-to-R-based splitting (NC-...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/2/208 |
| _version_ | 1818985162214473728 |
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| author | Min-Li Zeng Guo-Feng Zhang |
| author_facet | Min-Li Zeng Guo-Feng Zhang |
| author_sort | Min-Li Zeng |
| collection | DOAJ |
| description | To avoid solving the complex systems, we first rewrite the complex-valued nonlinear system to real-valued form (C-to-R) equivalently. Then, based on separable property of the linear and the nonlinear terms, we present a C-to-R-based Picard iteration method and a nonlinear C-to-R-based splitting (NC-to-R) iteration method for solving a class of large sparse and complex symmetric weakly nonlinear equations. At each inner process iterative step of the new methods, one only needs to solve the real subsystems with the same symmetric positive and definite coefficient matrix. Therefore, the computational workloads and computational storage will be saved in actual implements. The conditions for guaranteeing the local convergence are studied in detail. The quasi-optimal parameters are also proposed for both the C-to-R-based Picard iteration method and the NC-to-R iteration method. Numerical experiments are performed to show the efficiency of the new methods. |
| first_indexed | 2024-12-20T18:30:31Z |
| format | Article |
| id | doaj.art-a82305d7bf7d41e7b97f68f7a06fd87c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-20T18:30:31Z |
| publishDate | 2020-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a82305d7bf7d41e7b97f68f7a06fd87c2022-12-21T19:30:03ZengMDPI AGMathematics2227-73902020-02-018220810.3390/math8020208math8020208On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear EquationsMin-Li Zeng0Guo-Feng Zhang1School of Mathematics and Finance, Putian University, Putian 351100, ChinaSchool of Mathematics and Statistic, Lanzhou University, Lanzhou 730000, ChinaTo avoid solving the complex systems, we first rewrite the complex-valued nonlinear system to real-valued form (C-to-R) equivalently. Then, based on separable property of the linear and the nonlinear terms, we present a C-to-R-based Picard iteration method and a nonlinear C-to-R-based splitting (NC-to-R) iteration method for solving a class of large sparse and complex symmetric weakly nonlinear equations. At each inner process iterative step of the new methods, one only needs to solve the real subsystems with the same symmetric positive and definite coefficient matrix. Therefore, the computational workloads and computational storage will be saved in actual implements. The conditions for guaranteeing the local convergence are studied in detail. The quasi-optimal parameters are also proposed for both the C-to-R-based Picard iteration method and the NC-to-R iteration method. Numerical experiments are performed to show the efficiency of the new methods.https://www.mdpi.com/2227-7390/8/2/208weakly nonlinear equationsc-to-r preconditionerlocal convergencepicard iterationcomplex symmetric matrix. |
| spellingShingle | Min-Li Zeng Guo-Feng Zhang On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations Mathematics weakly nonlinear equations c-to-r preconditioner local convergence picard iteration complex symmetric matrix. |
| title | On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations |
| title_full | On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations |
| title_fullStr | On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations |
| title_full_unstemmed | On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations |
| title_short | On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations |
| title_sort | on c to r based iteration methods for a class of complex symmetric weakly nonlinear equations |
| topic | weakly nonlinear equations c-to-r preconditioner local convergence picard iteration complex symmetric matrix. |
| url | https://www.mdpi.com/2227-7390/8/2/208 |
| work_keys_str_mv | AT minlizeng onctorbasediterationmethodsforaclassofcomplexsymmetricweaklynonlinearequations AT guofengzhang onctorbasediterationmethodsforaclassofcomplexsymmetricweaklynonlinearequations |