矩阵方程组异类约束解的MCG1-3-5算法  

An MCG1-3-5 algorithm for heterogeneous constrained solutions of matrix equations

作　　者：陈世军 CHEN Shijun(School of Applied Technology,Fujian University of 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：《福建工程学院学报》2018年第4期365-371,共7页Journal of Fujian University of Technology

基　　金：福建工程学院教育科学研究项目(GB-RJ-17-65)

摘　　要：借鉴求线性矩阵方程组同类约束解的MCG算法(修正共轭梯度法),建立了求多个未知矩阵的线性矩阵方程组的一种异类约束解的MCG1-3-5算法,证明了该算法的收敛性。该算法不仅可以判断矩阵方程组的异类约束解是否存在,而且在有异类约束解,且不考虑舍入误差时,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,求得矩阵方程组的极小范数异类约束解。同时还能求取指定矩阵在该矩阵方程组异类约束解集合中的最佳逼近。算例表明,该算法有效。Based on the modified conjugate gradient method （MCG） for the same constrained solutions of linear matrix equations, a modified conjugate method MCG1-3-5 was established for heterogeneous constrained solutions of linear matrix equations with multiple unknown matrices. The convergence of this algorithm was also proved. This algorithm can not only judge the existence of heterogeneous constrained solutions of matrix equa- tions, but also obtain a set of such solutions within finite iterative steps in the absence of round off errors when there do exist heterogeneous constrained solutions. When a special initial matrix is selected, the heterogeneous constrained solution with a minimal norm can be obtained for the matrix equations. Meanwhile, the optimal approximation of the given matrix can be obtained in the set of the above-mentioned solutions. The example shows that the method is quite effective.

关 键 词：线性矩阵方程组 异类约束矩阵 MCG1-3-5算法 收敛性 最佳逼近 

分 类 号：O241.6[理学—计算数学]