重庆工商大学学报（自然科学版）

引用本文:	胡志增,杨春花.迭代算法求解矩阵方程埃尔米特双对称解(J/M/D/N,J:杂志，M：书，D：论文，N：报纸).期刊名称,2017，34（2）：6-11
	CHEN X. Adap tive slidingmode contr ol for discrete2ti me multi2inputmulti2 out put systems[ J ]. Aut omatica, 2006, 42(6): 4272-435

【打印本页】【下载PDF全文】【查看/发表评论】【EndNote】【RefMan】【BibTex】

←前一篇|后一篇→

过刊浏览高级检索

本文已被：浏览 848次下载 475次	码上扫一扫！
分享到：微信更多字体:加大+\|默认\|缩小-
迭代算法求解矩阵方程埃尔米特双对称解
胡志增,杨春花¹
湘潭大学数学与计算科学学院，湖南湘潭 411105

摘要:

通过构建一个迭代算法来求解复矩阵方程组最小〖WTBX〗F范数剩余问题：min〖JB(=〗〖JB((〗〖HL(1〗〖WTHX〗A1XB1+C1X〖TX-〗D1A2XB2+C2X〖TX-〗D2〖WTBX〗〖HL)〗〖JB))〗-〖JB((〗〖HL(1〗〖WTHX〗M1M2〖WTBX〗〖HL)〗〖JB))〗〖JB)=〗，〖JP〗其中〖WTHX〗X〖WTBX〗是埃尔米特双对称矩阵，即满足〖WTHX〗X〖WTBX〗=〖WTHX〗X〖WTBX〗H=〖WTHX〗S〖WTBX〗n〖WTHX〗XS〖WTBX〗n；在不考虑舍入误差的条件下，对于任意双埃尔米特矩阵〖WTHX〗X〖WTBX〗0，矩阵方程组的解都能在有限步内得到；最后，给出一个数值试验来检验算法的有效性.

关键词: 复矩阵方程迭代算法埃尔米特双对称解

DOI：

分类号:

基金项目:

An Iterative Algorithm for the Hermite Bisymmetric Solution to A Class of Complex Matrix Equations

HU Zhi zeng, YANG Chun hua

Abstract:

This paper is concerned with an iterative algorithm for solving the minimum Frobenius norm residual problem: 〖WTBX〗min〖JB(=〗〖JB((〗〖HL(1〗〖WTHX〗A1XB1+C1X〖TX-〗D1A2XB2+C2X〖TX-〗D2〖HL)〗〖JB))〗-〖JB((〗〖HL(1〗M1M2〖HL)〗〖JB))〗〖JB)=〗, 〖WT〗where 〖WTHX〗X〖WT〗 is a Hermite bisymmetric matrix which satisfies 〖WTHX〗X=X〖WTBX〗H=〖WTHX〗S〖WTBX〗n〖WTHX〗XS〖WTBX〗n〖WT〗. We can get the solution with finite iteration steps in the absence of roundoff errors for any initial Hermite bisymmetric matrix 〖WTHX〗X〖WT〗0 by this algorithm. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Key words: complex matrix equations iterative algorithm Hermite bisymmetric solution