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2011•Journal of Guizhou UniversityRequires access

The Convergence Analysis of the SOR Iterative Method in Preconditioned(I+S) on the Based Matrix Splitting

Gang Lei

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Abstract

The SOR iterative method was introduced to solve the large linear system Ax=b by using matrix iterative analysis and comparison theorems,make the nonsingular matrix P(preconditioned matrix) to left multiply the linear system two-sided.This paper adjoins in the parameter α to splitting the new coefficient matrix,then prove the improved method not only to accelerate the SOR iterative method,but also to excel the general preconditioned method.At last the numerical example is given.

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What this paper is about

The SOR iterative method was introduced to solve the large linear system Ax=b by using matrix iterative analysis and comparison theorems,make the nonsingular matrix P(preconditioned matrix) to left multiply the linear system two-sided.This paper adjoins in the parameter α to splitting the new coefficient matrix,then prove the improved method not only to accelerate the SOR iterative method,but also to excel the general preconditioned method.At last the numerical example is given.

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Available abstract

The SOR iterative method was introduced to solve the large linear system Ax=b by using matrix iterative analysis and comparison theorems,make the nonsingular matrix P(preconditioned matrix) to left multiply the linear system two-sided.This paper adjoins in the parameter α to splitting the new coefficient matrix,then prove the improved method not only to accelerate the SOR iterative method,but also to excel the general preconditioned method.At last the numerical example is given.

Key concepts: Invertible matrix, Iterative method, Coefficient matrix, Matrix splitting, Mathematics, Matrix (chemical analysis), Convergent matrix, Convergence (economics)

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