2005•Neimenggu Shi-da xuebao. Zhexue shehui kexue hanwen banRequires access

A Convergence Condition of the AOR Iteration for a Special Kind of Matrixs

Yang Ya-qiang

Abstract

A. Hadjidimos has proposed the accelerated over relaxation(AOR) iterative method for solving the linear systems and discussed the convergence of this method when the eigenvalues of Jacobi iterative matrix are real numbers.In this paper,the convergence of AOR iterative was discussed when the coefficient matrix of linear system is a (1,1) consistently ordered matrix and the eigenvalues of Jacobi iterative matrix are complex numbers.Then a convergence condition,which generalizes the results of A. Hadjidimos was obtained and a numerical example was given.

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