Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices
This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theore...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2021/8343207 |
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| _version_ | 1832560023101767680 |
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| author | Gashaye Dessalew Tesfaye Kebede Gurju Awgichew Assaye Walelign |
| author_facet | Gashaye Dessalew Tesfaye Kebede Gurju Awgichew Assaye Walelign |
| author_sort | Gashaye Dessalew |
| collection | DOAJ |
| description | This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration and obtain a greater rate of convergence than other previous methods. |
| format | Article |
| id | doaj-art-2bcef9d94ee64feb91299a274ebb73a0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2bcef9d94ee64feb91299a274ebb73a02025-02-03T01:28:32ZengWileyAbstract and Applied Analysis1085-33751687-04092021-01-01202110.1155/2021/83432078343207Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic MatricesGashaye Dessalew0Tesfaye Kebede1Gurju Awgichew2Assaye Walelign3Department of Mathematics, Bahir Dar University, Bahir Dar, EthiopiaDepartment of Mathematics, Bahir Dar University, Bahir Dar, EthiopiaDepartment of Mathematics, Bahir Dar University, Bahir Dar, EthiopiaDepartment of Mathematics, Bahir Dar University, Bahir Dar, EthiopiaThis paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration and obtain a greater rate of convergence than other previous methods.http://dx.doi.org/10.1155/2021/8343207 |
| spellingShingle | Gashaye Dessalew Tesfaye Kebede Gurju Awgichew Assaye Walelign Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices Abstract and Applied Analysis |
| title | Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices |
| title_full | Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices |
| title_fullStr | Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices |
| title_full_unstemmed | Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices |
| title_short | Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices |
| title_sort | generalized refinement of gauss seidel method for consistently ordered 2 cyclic matrices |
| url | http://dx.doi.org/10.1155/2021/8343207 |
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