M-P逆和加权M-P逆的有限迭代计算公式(英文)  

A Finite Iterative Computing Formula for M-P Inverse and Weighted M-P Inverse

作　　者：盛兴平[1] 陈果良[2] 

机构地区：[1]阜阳师范学院数学系,安徽阜阳236032 [2]华东师范大学数学系,上海200062

出　　处：《应用数学》2007年第2期336-344,共9页Mathematica Applicata

基　　金：Supported by the National Natural Sciences Foundation (10371044);the Science andTechnology Commission of Shanghai Municipality through grant (062112065, 04JC14031);the University Young Teacher Sciences Foundation of Anhui Province (2005jq1220zd)

摘　　要：本文,对于任意给定的矩阵A,我们给出了计算其M-P逆和加权M-P逆的有限迭代计算公式.根据这一迭代公式,当我们选取初始矩阵为X0=A#,则矩阵A的加权M-P逆AM+N在不考虑舍入误差的情况下,可以在有限迭代的情况得到,同样当我们选取初始矩阵X0=A*,其M-P逆A+亦可以在有限迭代下获得.最后我们用数值例子检验了我们算法的正确性.In this paper, a finite formula is presented to compute Moore-Penrose inverse A^＋ and weighted Moore-Penrose inverse A^＋MN of a given matrix A. By this iterative method, when taken the initial matrix Xo=A^#, the weighted M-P inverse A^＋MN can be obtained within finite iteration steps in absence of roundoff errors. In the same way, when taken X0=A^＊ , the M-P inverse A^＋ can also be got. Finally given numerical examples are shown that the iterative method is quite efficient.

关 键 词：M—P逆 加权M—P逆 有限迭代 

分 类 号：O151.21[理学—数学]