Improve refinement approach iterative method for solution linear equition of sparse matrices

Desi Vinsensia, Yulia Utami, Fathia Siregar, Muhammad Arifin
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Abstract

In this paper, systems of linear equations on sparse matrices investigated through modified improve method using Gauss-Seidel and successive overrelaxation (SOR) approach. Taking into adapted convergence rate on the Improve refinement Gauss-seidel outperformed the prior two Gauss-Seidel methods in terms of rate of convergence and number of iterations required to solve the problem by applying a modified version of the Gauss-Seidel approach. to observe the effectiveness of this method, the numerical example is given. The main findings in this study, that Gauss seidel improvement refinement gives optimum spectral radius and convergence rate. Similarly, the SOR improved refinement method gives. Considering their performance, using parameters such as time to converge, number of iterations required to converge and spectral radius level of accuracy. However, SOR works with relaxation values so that it greatly affects the convergence rate and spectral radius results if given greater than 1.
改进求解稀疏矩阵线性方程的细化方法迭代法
本文通过使用高斯-赛德尔和连续过度松弛(SOR)方法的改进方法,研究了稀疏矩阵上的线性方程组。考虑到改进细化的收敛率,高斯-赛德尔方法在收敛率和解决问题所需的迭代次数方面优于前两种高斯-赛德尔方法。为了观察这种方法的有效性,给出了数值示例。本研究的主要发现是,高斯-赛德尔改进细化法给出了最佳的谱半径和收敛速率。同样,SOR 改进细化方法也给出了最佳频谱半径和收敛率。在考虑它们的性能时,使用了收敛时间、收敛所需的迭代次数和光谱半径精度水平等参数。不过,SOR 采用松弛值工作,因此如果松弛值大于 1,会极大地影响收敛速度和光谱半径结果。
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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