新预条件下矩阵不同分裂的收敛性分析  

The Convergence Analysis of the Different Matrix Splitting under the New Pre-condition

作　　者：张红锋[1] 

机构地区：[1]江海职业技术学院基础部,江苏扬州225101

出　　处：《聊城大学学报（自然科学版）》2016年第1期13-18,共6页Journal of Liaocheng University:Natural Science Edition

基　　金：江苏省职业教育教学改革研究课题(ZYB104)

摘　　要：近年来对于求解线性方程组的技术有了很大的发展,特别是预条件技术的出现使得解线性方程组的速度有了很大的提高,在预条件技术中最主要的是怎样去找一个合适的预条件子,本文提出了一个新的预条件子,不但证明了当线性方程组的Ax=b系数矩阵为非奇异的M-矩阵和H-矩阵时,在新预条件子作用下它们的收敛性,还得到了在新预条件下PSOR、PJOR等的收敛速度明显快于以往经典SOR、JOR迭代法,从而证明了本文提出的新预条件子的优越性.In recent years there is a great development in solving the linear equations, especially af- ter the introduction of the pre-condition matrix, and the linear method＇s convergence rate accelerates greatly. What is the most important in the pre-condition technology is how to find a suitable pre-condi- tion. In this paper we propose a new pre-condition matrix, and when the Ax=b coefficient matrix is nonsingular irreducible M-matrix and H-matrix respectively we discuss the convergence analysis of not only the pre-conditioned ,but also we prove their convergence results under the new pre-condition, and demonstrate the convergence rate of PSOR and PJOR is clearly much faster than that of the classical SOR and JOR method, which show the superiority of our new per-condition iterative method in this paper.

关 键 词：预条件矩阵 M-矩阵 SOR迭代法 JOR迭代法 收敛性 

分 类 号：O13[理学—数学]