矩阵方程组异类约束解的MCG算法分析  

An iterative algorithm MCG for solving matrix equations over different constrained matrices

作　　者：陈世军 赖德清 CHEN Shijun;LAI Deqing(College of Applied Technology,Fujian University of Technology,Fuzhou Fujian 350001,China;Fujian Yongdeji Group CO.LTD,Fuzhou Fujian 350001,China)

机构地区：[1]福建工程学院应用技术学院,福建福州350001 [2]福建永德吉集团股份有限公司,福建福州350001

出　　处：《阜阳师范学院学报（自然科学版）》2019年第2期9-13,共5页Journal of Fuyang Normal University(Natural Science)

基　　金：福建省教育厅中青年科研项目(JZ180190);福建工程学院应用技术学院科研项目(YYJS-JB1808)资助

摘　　要：在变形共轭梯度法基础上,给出求解线性矩阵方程组的异类约束解的修正共轭梯度法(MCG算法),证明了该算法的收敛性。该算法不仅可以判断异类约束解是否存在,有解时可在有限步计算后求得矩阵方程组的一组异类约束解;选取特殊初始矩阵时,可求得矩阵方程组的极小范数异类约束解。算例表明该算法是可行的。On the base of the modified conjugate gradient,a modified conjugate method(MCG)is presented for solving a linear matrix equations over different constrained matrices.The convergence of this method is also given.We determine whether the matrix equations is consistent over different constrained matrices and obtain the solution within finite iterative steps in the absence of round off errors when the matrix equations is consistent,and the different constrained solution with least-norm can be got by choosing special initial matrices.The examples show that the method is quite efficient.

关 键 词：线性矩阵方程组 异类约束矩阵 MCG算法 

分 类 号：O241.6[理学—计算数学]