一类不相容矩阵方程对最小Frobenius范数问题的迭代算法(英)

华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (3): 30-36.

一类不相容矩阵方程对最小Frobenius范数问题的迭代算法(英)

徐相建^1,2, 王明辉², 魏木生²

1. 南通大学理学院, 江苏南通 226007 2. 华东师范大学数学系, 上海 200062

收稿日期:2007-06-25 修回日期:2007-09-17 出版日期:2008-05-25 发布日期:2008-05-25
通讯作者: 魏木生

Iterative algorithm for solving least Frobenius norm problem of an inconsistent matrix equation pair(English)

XU Xiang-jian^1,2, WANG Ming-hui², WEI Mu-sheng²

1. School of Science, Nantong University, Nantong Jiangsu 226007, China 2. Department of Mathematics, East China Normal University, Shanghai 2000621, China

Received:2007-06-25 Revised:2007-09-17 Online:2008-05-25 Published:2008-05-25
Contact: WEI Mu-sheng

摘要/Abstract

摘要： 提出了关于不相容矩阵方程对(AXB,CXD)=(E,F)最小Frobenius范数问题的一个迭代算法. 对于任意的初始矩阵X_0,在没有舍入误差的情况下, 运用此算法能在有限步内得到方程对在Frobienius范数意义下的最小解. 数值例子表明提出算法的有效性.

关键词: 迭代算法, Kronecker积, 矩阵方程对, 迭代算法, Kronecker积, 矩阵方程对

Abstract: This paper presented an iterative algorithm for solving the least Frobenius norm problem of inconsistent matrix equation pair (AXB,CXD)=(E,F) with a real matrix X. By this algorithm, for any (special) initial matrix X_0, a solution (the minimal Frobienius norm solution) can be obtained within finite iteration steps in the absence of roundoff errors. The numerical examples verify the efficiency of the algorithm.

Key words: Kronceker product, matrix equation pair, iterative algorithm, Kronceker product, matrix equation pair

中图分类号:

O24
O151

徐相建;王明辉;魏木生. 一类不相容矩阵方程对最小Frobenius范数问题的迭代算法(英)[J]. 华东师范大学学报(自然科学版), 2008, 2008(3): 30-36.

XU Xiang-jian;WANG Ming-hui;WEI Mu-sheng. Iterative algorithm for solving least Frobenius norm problem of an inconsistent matrix equation pair(English)[J]. Journal of East China Normal University(Natural Sc, 2008, 2008(3): 30-36.