A new preconditioned Richardson iterative method
In this paper, we propose a new iterative technique for solving an operator equation $Ax=y$ based on the Richardson iterative method. Then, by using the Chebyshev polynomials, we modify the proposed method to accelerate the convergence rate. Also, we present the results of some numerical experiments...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Publishing House of the Romanian Academy
2024-12-01
|
| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/1430 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850250702495940608 |
|---|---|
| author | Hassan Jamali Reza Pourkani |
| author_facet | Hassan Jamali Reza Pourkani |
| author_sort | Hassan Jamali |
| collection | DOAJ |
| description | In this paper, we propose a new iterative technique for solving an operator equation $Ax=y$ based on the Richardson iterative method.
Then, by using the Chebyshev polynomials, we modify the proposed method to accelerate the convergence rate.
Also, we present the results of some numerical experiments that demonstrate the efficiency and effectiveness
of the proposed methods compared to the existing, state-of-the-art methods. |
| format | Article |
| id | doaj-art-06faf165fa544195b57797a2e8d052e1 |
| institution | OA Journals |
| issn | 2457-6794 2501-059X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj-art-06faf165fa544195b57797a2e8d052e12025-08-20T01:58:07ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2024-12-0153210.33993/jnaat532-1430A new preconditioned Richardson iterative methodHassan Jamali0Reza Pourkani1Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, IranFaculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, IranIn this paper, we propose a new iterative technique for solving an operator equation $Ax=y$ based on the Richardson iterative method. Then, by using the Chebyshev polynomials, we modify the proposed method to accelerate the convergence rate. Also, we present the results of some numerical experiments that demonstrate the efficiency and effectiveness of the proposed methods compared to the existing, state-of-the-art methods.https://ictp.acad.ro/jnaat/journal/article/view/1430iterative methodRichardson iterationconvergence rateChebyshev polynomials |
| spellingShingle | Hassan Jamali Reza Pourkani A new preconditioned Richardson iterative method Journal of Numerical Analysis and Approximation Theory iterative method Richardson iteration convergence rate Chebyshev polynomials |
| title | A new preconditioned Richardson iterative method |
| title_full | A new preconditioned Richardson iterative method |
| title_fullStr | A new preconditioned Richardson iterative method |
| title_full_unstemmed | A new preconditioned Richardson iterative method |
| title_short | A new preconditioned Richardson iterative method |
| title_sort | new preconditioned richardson iterative method |
| topic | iterative method Richardson iteration convergence rate Chebyshev polynomials |
| url | https://ictp.acad.ro/jnaat/journal/article/view/1430 |
| work_keys_str_mv | AT hassanjamali anewpreconditionedrichardsoniterativemethod AT rezapourkani anewpreconditionedrichardsoniterativemethod AT hassanjamali newpreconditionedrichardsoniterativemethod AT rezapourkani newpreconditionedrichardsoniterativemethod |