矩阵方程AXB=C的中心对称最小二乘解及其最佳逼近的迭代算法  

An Iterative Method for the Least Squares Central Symmetric Solutions of the Matrix Equation AXB = C 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,西安710072

出　　处：《工程数学学报》2008年第6期1125-1128,共4页Chinese Journal of Engineering Mathematics

基　　金：陕西省自然科学基金(2004CS110002)

摘　　要：本文建立了求矩阵方程AXB=C的中心对称最小二乘解的迭代算法。在不考虑舍入误差时,对任意给定的初始中心对称矩阵,该算法能够在有限步迭代后得到此方程的中心对称最小二乘解。当选取特殊的初始矩阵时,可得到极小范数中心对称最小二乘解。另外,在上述解集合中也可得到给定矩阵的最佳逼近矩阵的表达式。An iterative method is presented to solve the least squares central symmetric solutions of the matrix equation AXB = C. By this iterative method, for any initial central symmetric 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 central symmetric matrices. In addition, its optimal approximation solution to a given matrix can be obtained.

关 键 词：矩阵方程 迭代算法 中心对称矩阵 最小二乘解 最佳逼近 

分 类 号：O241.6[理学—计算数学]