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2011•Journal of Wuyi UniversityRequires access

A New Comparison Theorem for the Preconditioned Gauss-Seidel Iterative Method

Huang Yong-hui

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Abstract

In this paper,the convergence analysis for a new preconditioned Gauss-Seidel iterative method was discussed.If the coefficient matrix is a nonsingular irreducible M-matrix,the convergence rate of this iterative method depends on the spectral radius of the original Gauss-Seidel method.Likewise,the spectral radius of the preconditioned Gauss-Seidel iterative method also depends on one of the preconditioned Gauss-Seidel methods.Finally,some numerical examples are given to explain our theoretical results.

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What this paper is about

In this paper,the convergence analysis for a new preconditioned Gauss-Seidel iterative method was discussed.If the coefficient matrix is a nonsingular irreducible M-matrix,the convergence rate of this iterative method depends on the spectral radius of the original Gauss-Seidel method.Likewise,the spectral radius of the preconditioned Gauss-Seidel iterative method also depends on one of the preconditioned Gauss-Seidel methods.Finally,some numerical examples are given to explain our theoretical results.

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Available abstract

In this paper,the convergence analysis for a new preconditioned Gauss-Seidel iterative method was discussed.If the coefficient matrix is a nonsingular irreducible M-matrix,the convergence rate of this iterative method depends on the spectral radius of the original Gauss-Seidel method.Likewise,the spectral radius of the preconditioned Gauss-Seidel iterative method also depends on one of the preconditioned Gauss-Seidel methods.Finally,some numerical examples are given to explain our theoretical results.

Key concepts: Spectral radius, Gauss–Seidel method, Mathematics, Iterative method, Applied mathematics, Invertible matrix, Convergence (economics), Rate of convergence

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