一类双变量矩阵方程广义自反Ls解的迭代算法  

An iterative algorithm for the generalized reflexive solution of the linear matrix equation with two matrix variables

作　　者：王娇[1] 张凯院[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072

出　　处：《纺织高校基础科学学报》2013年第1期130-136,共7页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(11071196)

摘　　要：借鉴求线性矩阵方程约束最小二乘(Ls)解的修正共轭梯度法,建立了求特殊类型的双矩阵变量线性矩阵方程的广义自反Ls解的迭代算法,证明了迭代算法的收敛性.利用该算法可在有限步迭代计算后求得矩阵方程的一组广义自反Ls解,选取特殊的初始矩阵时,可求得矩阵方程的极小范数广义自反Ls解.此外,还可求得在该矩阵方程的广义自反Ls解集合中对给定矩阵的最佳逼近.数值算例表明,迭代算法是有效的.Based on the method of the modified conjugate gradient to the linear matrix equation over constrained least square solution, an iterative algorithm is presented to find the generalized reflexive least square solution of the linear matrix equation which is a special type with two matrix variables. The convergence of the iterative method is proved. By this method, an generalized reflexive least square solution of the matrix equation can be obtained within finite iterative steps. And the generalized reflexive least square solution with least-norm can be got by choosing special initial matrices. Besides, the optimal approximation to any given matrix can be obtained in the set of the generalized reflexive least square solution. The numerical examples show that the iterative algorithm is quite efficient.

关 键 词：线性矩阵方程 广义自反矩阵 最小二乘解 极小范数解 迭代算法 最佳逼近 

分 类 号：O241.6[理学—计算数学]