矩阵方程组的最小二乘解及其最佳逼近的迭代算法  

An iterative method for the least squares solutions of a pair of matrix equations and its optimal approximation

作　　者：陈梅枝[1] 张凯院[1] 尚丽娜[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》2007年第1期45-50,共6页Basic Sciences Journal of Textile Universities

基　　金：陕西省自然科学基金资助项目(2004CS110002)

摘　　要：建立了求矩阵方程组AiXBi=Ci(i=1,2)的最小二乘解的迭代算法.不考虑舍入误差时,对任意给定的初始矩阵,该算法能够在有限步迭代计算后得到矩阵方程组的最小二乘解,给定特殊的初始矩阵时可得到极小范数最小二乘解.另外,在上述解集合中也可给出指定矩阵的最佳逼近矩阵.An iterative method is presented to solve the least squares solutions of a pair of matrix equations AiXBi = Ci （i = 1,2）. By this iterative method, for any initial matrix, a solution can be obtained within finite iterative steps in the absence of round off errors, and the solution with least norm can be obtained by choosing a special kind of initial matrix. In addition, its optimal approximation solution to a given matrix can be obtained.

关 键 词：矩阵方程组 迭代算法 最小二乘解 最佳逼近 

分 类 号：O241[理学—计算数学]