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The Convergence Discussion of the Gauss-Seidel Iterative Method in the New Matrix Splitting

Gang Lei

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Abstract

The Gauss-Seidel iterative method is discussed 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.The parameter α is pull in to splitting the new coefficient matix,then prove the improved method not only to accelerate the Gauss-Seidel iterative method,but also to excel the general preconditioned method.Last the numerical example is given.

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What this paper is about

The Gauss-Seidel iterative method is discussed 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.The parameter α is pull in to splitting the new coefficient matix,then prove the improved method not only to accelerate the Gauss-Seidel iterative method,but also to excel the general preconditioned method.Last the numerical example is given.

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Available abstract

The Gauss-Seidel iterative method is discussed 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.The parameter α is pull in to splitting the new coefficient matix,then prove the improved method not only to accelerate the Gauss-Seidel iterative method,but also to excel the general preconditioned method.Last the numerical example is given.

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

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