Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices

Q3 Mathematics

Abstract and Applied Analysis Pub Date : 2021-05-31 DOI:10.1155/2021/8343207

Gashaye Dessalew, T. Kebede, Gurju Awgichew, Assaye Walelign

引用次数: 1

Abstract

This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration and obtain a greater rate of convergence than other previous methods.

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一致有序2循环矩阵的Gauss-Seidel方法的广义改进

本文在考虑一致有序2循环矩阵的情况下，对求解线性方程组的Gauss-Seidel方法进行了广义改进。用有限差分法求解微分方程，得到了一致有序的2循环矩阵。引入了合适的定理来验证该方法的收敛性。为了观察该方法的有效性，给出了几个数值算例。研究指出，利用高斯-塞德尔方法的广义改进，我们得到了一个问题的最小迭代次数的解，并获得了比其他方法更大的收敛速度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Abstract and Applied Analysis 数学-数学

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

3.5 months

期刊介绍： Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.