A Study on the Convergence Analysis of the Inexact Simplified Jacobi–Davidson Method
The Jacobi–Davidson iteration method is very efficient in solving Hermitian eigenvalue problems. If the correction equation involved in the Jacobi–Davidson iteration is solved accurately, the simplified Jacobi–Davidson iteration is equivalent to the Rayleigh quotient iteration which achieves cubic c...
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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/10.1155/2021/2123897 |
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| _version_ | 1832560732729769984 |
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| author | Jutao Zhao Pengfei Guo |
| author_facet | Jutao Zhao Pengfei Guo |
| author_sort | Jutao Zhao |
| collection | DOAJ |
| description | The Jacobi–Davidson iteration method is very efficient in solving Hermitian eigenvalue problems. If the correction equation involved in the Jacobi–Davidson iteration is solved accurately, the simplified Jacobi–Davidson iteration is equivalent to the Rayleigh quotient iteration which achieves cubic convergence rate locally. When the involved linear system is solved by an iteration method, these two methods are also equivalent. In this paper, we present the convergence analysis of the simplified Jacobi–Davidson method and present the estimate of iteration numbers of the inner correction equation. Furthermore, based on the convergence factor, we can see how the accuracy of the inner iteration controls the outer iteration. |
| format | Article |
| id | doaj-art-5a5dc12e2d424fc2b951fb6cfd8ab4cf |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5a5dc12e2d424fc2b951fb6cfd8ab4cf2025-02-03T01:26:54ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/2123897A Study on the Convergence Analysis of the Inexact Simplified Jacobi–Davidson MethodJutao Zhao0Pengfei Guo1Department of MathematicsSchool of Mathematics and StatisticsThe Jacobi–Davidson iteration method is very efficient in solving Hermitian eigenvalue problems. If the correction equation involved in the Jacobi–Davidson iteration is solved accurately, the simplified Jacobi–Davidson iteration is equivalent to the Rayleigh quotient iteration which achieves cubic convergence rate locally. When the involved linear system is solved by an iteration method, these two methods are also equivalent. In this paper, we present the convergence analysis of the simplified Jacobi–Davidson method and present the estimate of iteration numbers of the inner correction equation. Furthermore, based on the convergence factor, we can see how the accuracy of the inner iteration controls the outer iteration.http://dx.doi.org/10.1155/2021/2123897 |
| spellingShingle | Jutao Zhao Pengfei Guo A Study on the Convergence Analysis of the Inexact Simplified Jacobi–Davidson Method Journal of Mathematics |
| title | A Study on the Convergence Analysis of the Inexact Simplified Jacobi–Davidson Method |
| title_full | A Study on the Convergence Analysis of the Inexact Simplified Jacobi–Davidson Method |
| title_fullStr | A Study on the Convergence Analysis of the Inexact Simplified Jacobi–Davidson Method |
| title_full_unstemmed | A Study on the Convergence Analysis of the Inexact Simplified Jacobi–Davidson Method |
| title_short | A Study on the Convergence Analysis of the Inexact Simplified Jacobi–Davidson Method |
| title_sort | study on the convergence analysis of the inexact simplified jacobi davidson method |
| url | http://dx.doi.org/10.1155/2021/2123897 |
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