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Note on the convergence of AOR and 2PPJ iterative methods

Qingbing Liu, Guoliang Chen

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Abstract

This paper analyzed the convergence of preconditioned AOR and 2PPJ iterative methods when the coefficient matrix is an M-matrix,and pointed out some errors of known results and established correct convergence theorems.Meanwhile,by the H-splitting theory,the convergence of the preconditioned AOR iterative method for the case of the coefficient matrix being an H-matrix was discussed and the convergence interval of parameters was given.

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What this paper is about

This paper analyzed the convergence of preconditioned AOR and 2PPJ iterative methods when the coefficient matrix is an M-matrix,and pointed out some errors of known results and established correct convergence theorems.Meanwhile,by the H-splitting theory,the convergence of the preconditioned AOR iterative method for the case of the coefficient matrix being an H-matrix was discussed and the convergence interval of parameters was given.

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Available abstract

This paper analyzed the convergence of preconditioned AOR and 2PPJ iterative methods when the coefficient matrix is an M-matrix,and pointed out some errors of known results and established correct convergence theorems.Meanwhile,by the H-splitting theory,the convergence of the preconditioned AOR iterative method for the case of the coefficient matrix being an H-matrix was discussed and the convergence interval of parameters was given.

Key concepts: Convergence (economics), Matrix (chemical analysis), Mathematics, Iterative method, Applied mathematics, Coefficient matrix, Convergence tests, Mathematical optimization

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