Convergence and Comparison Theorems of the Modified Gauss-Seidel Method

Zhouji Chen

doi:10.5281/zenodo.2658399

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Convergence and Comparison Theorems of the Modified Gauss-Seidel Method

Zhouji Chen

Year: 2013 Journal: Zenodo (CERN European Organization for Nuclear Research) Publisher: European Organization for Nuclear Research

DOI: 10.5281/zenodo.2658399

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Abstract

In this paper, the modified Gauss-Seidel method with the new preconditioner for solving the linear system $Ax=b$, where $A$ is a nonsingular $M$-matrix with unit diagonal, is considered. The convergence property and the comparison theorems of the proposed method are established. Two examples are given to show the efficiency and effectiveness of the modified Gauss-Seidel method with the presented new preconditioner.

Keywords:

Convergence (economics) Preconditioner Invertible matrix Property (philosophy) Linear system Iterative method

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Matrix Theory and Algorithms

Physical Sciences → Computer Science → Computational Theory and Mathematics

Iterative Methods for Nonlinear Equations

Physical Sciences → Mathematics → Numerical Analysis

Advanced Optimization Algorithms Research

Physical Sciences → Mathematics → Numerical Analysis

Convergence and Comparison Theorems of the Modified Gauss-Seidel Method

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