矩阵最大线性无关子块提取研究  

The Extraction of the Largest Linearly Independent Block of a Matrix

作　　者：王芳 马艳丽[2] WANG Fang;MA Yanli(Public Curriculum Department,Anhui Foreign Languages University,Hefei,Anhui 231200;General Education Department,Anhui Xinhua University,Hefei,Anhui 230088)

机构地区：[1]安徽外国语学院公共基础课教学部,安徽合肥231200 [2]安徽新华学院通识教育部,安徽合肥230088

出　　处：《玉溪师范学院学报》2020年第6期6-10,共5页Journal of Yuxi Normal University

基　　金：安徽省高校自然科学重点研究项目“求解大型稀疏线性系统的若干迭代算法”(KJ2018A0610);安徽省高校自然科学重点研究项目“接种和剔除混合控制策略影响下传染病模型的全局稳定性研究及应用”(KJ2019A0875).

摘　　要：针对构造一种基于恰当分裂的预条件子时,需要提取最大线性无关子块和相应的置换矩阵的问题,给出了相应的算法,并通过数值实验验算算法的有效性和提取一些大型稀疏矩阵最大无关子块所需要的CPU运行时间,最后使用此算法构造了基于恰当分裂的预条件子,并使用预条件QMR算法和预条件GMRES算法验证预条件子的有效性.When constructing a preconditioner based on proper splitting,it is necessary to extract the maximal linearly independent block and the corresponding permutation matrix.In this paper,a corresponding algorithm is proposed to solve this problem.Numerical experiments are carried out to verify the effectiveness of the algorithm and the CPU running time required to extract the maximal linearly independent block of some large sparse matrices.Finally,a preconditioner based on proper splitting is constructed by using this algorithm,and two preconditioned QMR algorithms and preconditioned GMRES algorithm are used to verify the ef fectiveness of the preconditioner.

关 键 词：最大线性无关子块 置换矩阵 线性方程组 预条件子 

分 类 号：O241.6[理学—计算数学]