一种求解线性方程组的Gauss-Seidel变体方法  

A Variant Method of Gauss-Seidel for Solving a System of Linear Equations

作　　者：徐丽华[1] 沈丹桂[1] 王薇[1] 王文博[1] Xu Lihua Shen Dangui Wang Wei Wang Wenbo(College of Mathematics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001)

机构地区：[1]嘉兴学院数理与信息工程学院,浙江嘉兴314001

出　　处：《嘉兴学院学报》2016年第6期23-28,共6页Journal of Jiaxing University

基　　金：浙江省自然科学青年基金项目(LQ14A010013);浙江省大学生科研创新团队资助项目(2015R417027)

摘　　要：随着并行计算的快速发展,设计求解线性方程组的并行算法已是科学计算中的一个热点问题.Jacobi方法和Gauss-Seidel方法是求解线性方程组的常用迭代法,前者的并行度大,后者的收敛速度快.本文综合这两种方法的优势,构造了Gauss-Seidel变体方法,并对其收敛性进行了分析.此外,在Matlab环境下,我们对Gauss-Seidel变体方法实现了并行,通过数值实验验证了该并行算法的有效性.With the rapid development of parallel computation, the design of parallel algorithms for solving the linear system of equations has been a hot issue in scientific computing. The Jacobi method and Gauss-Seidel method are common iterative ones for solving linear equations. The parallel degree of the former is large, and the convergence rate of the latter is fast. Integrating advantages of these two methods, this method constructs a variant method of the Gauss-Seidel, and analyzes its convergence. In addition, we apply the parallel algorithm of this variant method in Matlab environment, and prove the efficiency of algorithm by implementing numerical ex- periments.

关 键 词：线性方程组 JACOBI方法 Gauss-Seidel方法 Gauss-Seidel变体方法 并行算法 

分 类 号：O241.6[理学—计算数学]