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2011•Journal of Hanshan Normal UniversityRequires access

A New Comparison Theorem for the Preconditioned Jacobi Iterative Method

Huang Yong-hui

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Abstract

In this paper,the convergence analysis for a new preconditioned Jacobi iterative method was discussed.If the coefficient matrix is the strictly dominant L-matrix,the convergence rate of the preconditioned Jacobi iterative method is faster than one of the Jacobi methods.In addition,the spectral radius of this method is monotonically decreasing.Last,a numerical example is used to verify the correctness of our theoretical results.

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What this paper is about

In this paper,the convergence analysis for a new preconditioned Jacobi iterative method was discussed.If the coefficient matrix is the strictly dominant L-matrix,the convergence rate of the preconditioned Jacobi iterative method is faster than one of the Jacobi methods.In addition,the spectral radius of this method is monotonically decreasing.Last,a numerical example is used to verify the correctness of our theoretical results.

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Available abstract

In this paper,the convergence analysis for a new preconditioned Jacobi iterative method was discussed.If the coefficient matrix is the strictly dominant L-matrix,the convergence rate of the preconditioned Jacobi iterative method is faster than one of the Jacobi methods.In addition,the spectral radius of this method is monotonically decreasing.Last,a numerical example is used to verify the correctness of our theoretical results.

Key concepts: Spectral radius, Jacobi method, Correctness, Jacobi eigenvalue algorithm, Iterative method, Mathematics, Applied mathematics, Convergence (economics)

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