An iterative method for the reflezive solutions of the matriz equation A1X1B1+A2X2B2+…+A1X1B1 = C

摘要：

In this paper,an iterative method is constructed to find the reflexive solution of the matrix equation A1X1B1+A2X2B2+…+ A1X1B1=C where X1, X2,..., X1 is real matrices group. By this iterative method,the solvability of the matrix equation can be judged automatically. When the matrix equation is consistent,for any initial reflexive matrix groupX(0)1,X(0)2,...,X(0)1,a reflexive solution group can be obtained within finite iteration steps in the absence of roundoff errors, and the least norm reflexive solution group can be obtained by choosing a special kind of initial reflexive matrix group. In addition, the optimal approximation reflexive solution group to a given reflexive matrix group (X)1,(X)2,…,(X)tin Frobenius norm can be obtained by finding the least norm reflexive solution group of new matrix equation A1X1B1+ A2X2B2 +…+ A1X1B1=C, where (C)=C-A1X1B1-A2X2B2……A1X1B1.

关键词： Iterative method matriz equation reflezive solution group least-norm solution group optimal approzimation solution

作者: Zhuohua Peng Jinwang Liu

作者单位: School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan ,Hunan, 411201, P.R.China

会议类型: 国际会议

会议名称: The Third International Workshop on Applied Matriz Theory(第三届国际矩阵分析与应用会议)

会议地点: 杭州

会议语种:英文

页码: 899-902

在线出版日期: 2009-07-09（万方平台首次上网日期，不代表论文的发表时间）