A New Version of the Accelerated Overrelaxation Iterative Method

Hadjidimos (1978) proposed a classical accelerated overrelaxation (AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant, L-matrices, and consistently orders matrices. In this...

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Main Authors: Shi-Liang Wu, Yu-Jun Liu
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/725360
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author Shi-Liang Wu
Yu-Jun Liu
author_facet Shi-Liang Wu
Yu-Jun Liu
author_sort Shi-Liang Wu
collection DOAJ
description Hadjidimos (1978) proposed a classical accelerated overrelaxation (AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant, L-matrices, and consistently orders matrices. In this paper, a new version of the AOR method is presented. Some convergence results are derived when the coefficient matrices are irreducible diagonal dominant, H-matrices, symmetric positive definite matrices, and L-matrices. A relational graph for the new AOR method and the original AOR method is presented. Finally, a numerical example is presented to illustrate the efficiency of the proposed method.
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institution DOAJ
issn 1110-757X
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publishDate 2014-01-01
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spelling doaj-art-4bbc304f142a40b68a2040b46e51ab892025-08-20T03:20:13ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/725360725360A New Version of the Accelerated Overrelaxation Iterative MethodShi-Liang Wu0Yu-Jun Liu1School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, ChinaSchool of Mathematics and Statistics, Anyang Normal University, Anyang 455000, ChinaHadjidimos (1978) proposed a classical accelerated overrelaxation (AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant, L-matrices, and consistently orders matrices. In this paper, a new version of the AOR method is presented. Some convergence results are derived when the coefficient matrices are irreducible diagonal dominant, H-matrices, symmetric positive definite matrices, and L-matrices. A relational graph for the new AOR method and the original AOR method is presented. Finally, a numerical example is presented to illustrate the efficiency of the proposed method.http://dx.doi.org/10.1155/2014/725360
spellingShingle Shi-Liang Wu
Yu-Jun Liu
A New Version of the Accelerated Overrelaxation Iterative Method
Journal of Applied Mathematics
title A New Version of the Accelerated Overrelaxation Iterative Method
title_full A New Version of the Accelerated Overrelaxation Iterative Method
title_fullStr A New Version of the Accelerated Overrelaxation Iterative Method
title_full_unstemmed A New Version of the Accelerated Overrelaxation Iterative Method
title_short A New Version of the Accelerated Overrelaxation Iterative Method
title_sort new version of the accelerated overrelaxation iterative method
url http://dx.doi.org/10.1155/2014/725360
work_keys_str_mv AT shiliangwu anewversionoftheacceleratedoverrelaxationiterativemethod
AT yujunliu anewversionoftheacceleratedoverrelaxationiterativemethod
AT shiliangwu newversionoftheacceleratedoverrelaxationiterativemethod
AT yujunliu newversionoftheacceleratedoverrelaxationiterativemethod