矩阵方程∑_i^l=1_A_iX_iB_i=C的最小二乘广义双对称解  

The Least-Squares Generalized Bisymmetric Solutions of the Matrix Equation ∑_i^l =1_A_iX_iB_i=C

作　　者：彭卓华[1] 辛会敏[1] 

机构地区：[1]湖南科技大学数学与计算科学学院,湖南湘潭411201

出　　处：《湘潭大学自然科学学报》2014年第1期16-20,共5页Natural Science Journal of Xiangtan University

基　　金：国家自然科学基金项目(11071062);湖南省科技厅资助项目(2012FJ3048)

摘　　要：该文通过使用投影技术构造了一种算法求最小二乘问题min‖∑l i=1AiXiBi-C‖的广义双对称解.通过该方法,经过有限步迭代,得到广义双对称解和最小范数解.证明了其的收敛性.数值例子表明了该方法的有效性.In this paper, an algorithm is presented to find the least-squares generalized bisymmetric solu- tions of the matrix equation∑li=1AiXiBi=Cby applying projection technique. The algorithm produces suit- able generalized bisymmetric matrix [X1 ,X2 ,……,Xl ] such that I∑li=1AiXiBi=C is minimized within fi- nite iteration steps, and the least norm solution can also be obtained. We show that the algorithm is stable. Numerical experiments are given to show that the algorithm is efficient.

关 键 词：最小二乘问题 对称解 广义 矩阵方程 最小范数解 有限步迭代 最小二乘解 投影技术 

分 类 号：O151.21[理学—数学]