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...

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Main Authors: Hassan Jamali, Reza Pourkani
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
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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
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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