一种改进的求解大型线性方程组的Jacobi迭代法

doi:10.6040/j.issn.1671-9352.0.2019.003

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (6): 122-126.doi: 10.6040/j.issn.1671-9352.0.2019.003

• • 上一篇

一种改进的求解大型线性方程组的Jacobi迭代法

王燕荣¹,陈云兰²

1.太原师范学院数学系, 山西晋中 030619;2.天津大学数学学院, 天津 300072

发布日期:2020-06-01
作者简介:王燕荣(1979— ),女,硕士研究生,讲师,研究方向为数学课程论、最优化方法与算法. E-mail:wangyr0202@163.com
基金资助:
国家自然科学基金资助项目(61503276)

A modified Jacobi iterative method for large-size linear systems

WANG Yan-rong¹, CHEN Yun-lan²

1. Department of Mathematics, Taiyuan Normal University, Jinzhong 030619, China;
2. School of Mathematics, Tianjin University, Taijin 300072, China

Published:2020-06-01

摘要/Abstract

摘要： 针对求解大型线性方程组提出了一种新的Jacobi迭代法。其思想是用Jacobi迭代法得到的当前点和上一步迭代点的组合得到下一步迭代点,并且通过求解最小二乘优化问题求得最佳组合因子。在与经典的Jacobi迭代法相同的条件下,证明了这种最优外插Jacobi迭代法的全局收敛性,进一步的数值实验也验证了新算法的有效性。

关键词: 线性方程组, Jacobi迭代法, 最优组合因子

Abstract: An improved Jacobi method is proposed for solving large-size linear system. The improvement of the proposed method is to use the combination of the current point obtained by Jacobi method and the previous point to get the new point, to get the optimal factor of linear combination by solving the least square optimization. Under the same conditions as the classic Jacobi method, the global convergence of this method is proved, the computational results show the effectiveness of this method.

Key words: linear systems, Jacobi method, optimal factor of linear combination

中图分类号:

O241.6

王燕荣,陈云兰. 一种改进的求解大型线性方程组的Jacobi迭代法[J]. 《山东大学学报(理学版)》, 2020, 55(6): 122-126.

WANG Yan-rong, CHEN Yun-lan. A modified Jacobi iterative method for large-size linear systems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(6): 122-126.

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一种改进的求解大型线性方程组的Jacobi迭代法

A modified Jacobi iterative method for large-size linear systems

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