2011•Unpublished venueRequires access

On the Application of Column Pivot Element in Gauss-Seidel and SOR Iteration

Qin Yan-mei

Abstract

Combining the iterative method and the column pivoting,two improved iterative methods for linear equations is given,based on the Gauss-Seidel iterative method and SOR iterative method.The improved method expands the range to the Gauss-Seidel iterative method and SOR iterative method,which brings practical application value.By writing MATLAB program,the convergence of Gauss-Seidel iterative and the SOR iterative methods are verified.Meanwhile,through to comparison of the convergence speed of the classical Gauss-Seidel iterative,SOR iterative method,the improved Gauss-Seidel iterative method,and SOR iterative method,a conclusion is given: the two new iterative methods has a wider scope,a faster convergence speed.

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Key concepts: Gauss–Seidel method, Iterative method, Convergence (economics), Mathematics, Successive over-relaxation, Mathematical optimization, Local convergence, Computer science