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2012•Journal of Shanxi Datong UniversityRequires access

Convergence of the AOR for Consistently Ordered Matrix

Wang Zhen-fang

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Abstract

In this paper,the Condition of convergence of AOR iterative was discussed when the coefficient matrix of a linear system is a(1,1) consistently ordered matrix and the eigenvalues of its Jacobi matrix in three cases,and the optimum parameters of its AOR iterative method are given when the eigenvalues of its Jacobi matrix are all pure imaginares or are all real numbers.In adition,a examples is given for illustrating the results.

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What this paper is about

In this paper,the Condition of convergence of AOR iterative was discussed when the coefficient matrix of a linear system is a(1,1) consistently ordered matrix and the eigenvalues of its Jacobi matrix in three cases,and the optimum parameters of its AOR iterative method are given when the eigenvalues of its Jacobi matrix are all pure imaginares or are all real numbers.In adition,a examples is given for illustrating the results.

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Available abstract

In this paper,the Condition of convergence of AOR iterative was discussed when the coefficient matrix of a linear system is a(1,1) consistently ordered matrix and the eigenvalues of its Jacobi matrix in three cases,and the optimum parameters of its AOR iterative method are given when the eigenvalues of its Jacobi matrix are all pure imaginares or are all real numbers.In adition,a examples is given for illustrating the results.

Key concepts: Eigenvalues and eigenvectors, Mathematics, Convergence (economics), Matrix (chemical analysis), Applied mathematics, Jacobi method, Iterative method, Jacobi eigenvalue algorithm

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