最小二乘广义逆求解方法研究及应用  

Research and application on the solution of the least square generalized inverses

作　　者：张亚飞[1] 韩凯歌[1] 沈艳[1] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《应用科技》2014年第3期60-63,共4页Applied Science and Technology

基　　金：国家自然科学基金资助项目(11002037)

摘　　要：广义线性系统是自动控制理论的一个重要组成部分,在研究广义线性系统的诸多问题中常常需要计算系统状态矩阵的广义逆,因而广义逆矩阵的求解方法就显得格外重要。文中给出了矩阵最小二乘广义逆的2种求解方法,分别证明了2种方法的正确性,最后举出广义线性控制系统的实际算例。通过用这2种方法求解系统状态矩阵的最小二乘广义逆,验证了所给方法的有效性和可行性,同时方法简单易行,适合计算机编程计算。A generalized linear system is an important part of automatic control theory , and the generalized inverse of status matrix needs to be calculated usually in the research of generalized linear system , thus the solving methods of generalized inverse is especially significant .This paper discusses two methods to get the least square generalized inverse of matrix , both the processes of proof are given .A generalized linear system as an example shows that the two methods are valid and practical .The least square generalized inverse is obtained by the two methods respective-ly.It also validates that the two methods are simple and easy , suitable for programming and computing .

关 键 词：广义系统 Moore-Penrose方程 矩阵广义逆 最小二乘广义逆 行式 

分 类 号：O151.21[理学—数学]