矩阵方程组一种异类约束解的MCG1-2-3-4算法  

An Iterative Algorithm MCG1-2-3-4 for Solving Matrix Equations over different Constrained Matrices

作　　者：陈世军 CHEN Shi-jun(Fujian university of technology college of Applied Technology,Fuzhou 350001,China)

机构地区：[1]福建工程学院应用技术学院,福建福州350001

出　　处：《牡丹江师范学院学报（自然科学版）》2018年第4期1-9,共9页Journal of Mudanjiang Normal University：Natural Sciences Edition

基　　金：2018年福建省教育厅中青年教育科研项目(信息化专项)重点课题(JZ180190);福建工程学院应用技术学院2018年科研项目(YYJS-JB1808)

摘　　要：建立求含多个未知矩阵方程组的对称、反对称、中心对称和中心反对称解的修正共轭梯度算法.该算法可以判断矩阵方程组的对称、反对称、中心对称和中心反对称解是否存在,在约束解存在时,不考虑舍入误差情况下,能求得矩阵方程组的一组异类约束解;选取特殊初始矩阵时,可求得该方程组的极小范数解;给定矩阵可以在约束解集合中,求出其最佳逼近矩阵.数值实验验证了该算法的可行性.A modified conjugate method MCG1-2-3-4 is presented for solving a linear matrix equations with several unknown matrices about symmetric matrix, antisymmetric matrix,central symmetric matrix and central antisymmetric matrix. By this method, we not only can judge whether the matrix equations is consistent over different constrained matrices, but also can obtain the solution 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. In addition, the optimal approximation matrix of the given matrix can be obtained in the set of the different constrained solution. The numerical example show that the method is quite efficient.

关 键 词：异类约束矩阵 修正共轭梯度法 收敛性 最佳逼近 

分 类 号：O211.6[理学—概率论与数理统计]