2012•Journal of North University of ChinaRequires access

A New Preconditioned Gauss-Seidel Iterative Method and Its Convergence

Yang Jin

Abstract

A new preconditioned matrix was introduced for solving linear systems with Gauss-Seidel iterative method.Under the condition that the coefficient matrix being an M-matrix,which is widely used,the comparison theorem between preconditioned Gauss-Seidel iterative method and classic Gauss-Seidel iterative method was given.The preconditioned Gauss-Seidel iterative method is convergent and it accelerates the convergent speed of classic Gauss-Seidel iterative method.It showed that newly proposed preconditioned Gauss-Seidel iterative method is superior to the Gauss-Seidel iterative method mentioned.A numerical example was given to verify the effectiveness of the conclusions.

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Key concepts: Gauss–Seidel method, Iterative method, Mathematics, Convergence (economics), Matrix (chemical analysis), M-matrix, Coefficient matrix, Applied mathematics