Reza BEHZADI.A New Class AOR Preconditioner for $L$-Matrices[J].数学研究及应用,2019,39(1):101~110
A New Class AOR Preconditioner for $L$-Matrices
A New Class AOR Preconditioner for $L$-Matrices
投稿时间:2018-02-26  修订日期:2018-08-12
DOI:10.3770/j.issn:2095-2651.2019.01.010
中文关键词:  AOR iterative method  $L$-matrix  irreducible matrix  spectral radius  preconditioner  iteration matrix
英文关键词:AOR iterative method  $L$-matrix  irreducible matrix  spectral radius  preconditioner  iteration matrix
基金项目:
作者单位
Reza BEHZADI Department of Mathematics, College of Science, Shiraz University, Shiraz, Iran 
摘要点击次数: 78
全文下载次数: 110
中文摘要:
      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. Several preconditioned AOR methods have been proposed to solve system of linear equations $Ax = b$, where $A \in \mathbb{R}^{n\times n}$ is an $L$-matrix. In this work, we introduce a new class preconditioners for solving linear systems and give a comparison result and some convergence result for this class of preconditioners. Numerical results for corresponding preconditioned GMRES methods are given to illustrate the theoretical results.
英文摘要:
      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. Several preconditioned AOR methods have been proposed to solve system of linear equations $Ax = b$, where $A \in \mathbb{R}^{n\times n}$ is an $L$-matrix. In this work, we introduce a new class preconditioners for solving linear systems and give a comparison result and some convergence result for this class of preconditioners. Numerical results for corresponding preconditioned GMRES methods are given to illustrate the theoretical results.
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