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2012•Journal of Jinggangshan UniversityRequires access

THE CONVERGENCE DISSCUSSION OF THE PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHOD WITH A MORE GENERAL SPLITTING

Shiguang Zhang

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Abstract

Using the Gauss-Seidel iterative method for the solution of the linear equations,the convergence of the Gauss-Seidel iterative method is discussed under a type of preconditioned matrix.With a more general splitting,we compare the convergence of the preconditioned Gauss-Seidel iterative method and the corresponding Gauss-Seidel iterative method.Furthermore,we get some comparison theorems.Finally,a numerical example is given to illustrate the validity of the conclusions.

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What this paper is about

Using the Gauss-Seidel iterative method for the solution of the linear equations,the convergence of the Gauss-Seidel iterative method is discussed under a type of preconditioned matrix.With a more general splitting,we compare the convergence of the preconditioned Gauss-Seidel iterative method and the corresponding Gauss-Seidel iterative method.Furthermore,we get some comparison theorems.Finally,a numerical example is given to illustrate the validity of the conclusions.

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Available abstract

Using the Gauss-Seidel iterative method for the solution of the linear equations,the convergence of the Gauss-Seidel iterative method is discussed under a type of preconditioned matrix.With a more general splitting,we compare the convergence of the preconditioned Gauss-Seidel iterative method and the corresponding Gauss-Seidel iterative method.Furthermore,we get some comparison theorems.Finally,a numerical example is given to illustrate the validity of the conclusions.

Key concepts: Gauss–Seidel method, Iterative method, Convergence (economics), Mathematics, Applied mathematics, Gauss, Matrix (chemical analysis), Mathematical optimization

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