求矩阵方程组的反对称最小二乘解的递推算法  

An Iteration Method for the Least Squares Skew-Symmetric Solutions of Matrix Equations

作　　者：刘莉[1,2] 张凯院[2] 王文帅[1] 

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021 [2]西北工业大学应用数学系,陕西西安710072

出　　处：《数学的实践与认识》2010年第18期190-197,共8页Mathematics in Practice and Theory

基　　金：宁夏大学自然科学基金(ZR200805)

摘　　要：讨论了矩阵方程组A_1XB_1=D_1,A_2XB_2=D_2反对称最小二乘解的递推算法,该算法不仅能够用于计算反对称最小二乘解,而且在选取特殊的初始矩阵时,算法能够求出矩阵方程组的极小范数反对称最小二乘解,以及对给定的矩阵进行最佳逼近的反对称解.This paper discusses the least squares skew-symmetric solutions of the matrix equations A1×BI=D1, A2×B2=D2. By this recursive algorithm, the solution with least norm can be obtained by choosing a special kind of initial skew-symmetric matrix. In addition, the unique optimal approximation solution to a given matrix in Frobenius norm can be obtained by finding the least norm solution of the new minimum residual problem.

关 键 词：反对称最小二乘解 极小范数解 最佳逼近解 

分 类 号：O241.6[理学—计算数学]