华东师范大学学报(自然科学版) ›› 2005, Vol. 2005 ›› Issue (5/6): 72-78.

• 数学 统计学 • 上一篇    下一篇

L-零矩阵的广义Bott-Duffin逆的扰动分析(II)(英)

张新发1,陈果良2,薛以锋1

  

  1. 1. 华东理工大学 数学系, 上海 200237; 2.华东师范大学 数学系, 上海 200062
  • 收稿日期:2003-09-17 修回日期:2003-11-05 出版日期:2005-12-31 发布日期:2005-12-31
  • 通讯作者: 张新发

Perturbation Analysis of the Generalized Bott-Duffin Inverse of L-zero Matrices(II)(English)

ZHANG Xin-fa1, CHEN Guo-liang2, XUE Yi-feng1   

  1. 1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China; 2. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2003-09-17 Revised:2003-11-05 Online:2005-12-31 Published:2005-12-31
  • Contact: ZHANG Xin-fa

摘要： 设L是Fn的子空间 PL是Fn到L上的正交投影, 其中F=C 或 R. 设A是一个n× n的矩阵.本文给出了广义Bott-Duffin逆A(L)(+)=PL(APL+I-PL)+当A和L都有小扰动时的扰动分析. 利用这个结果, 建立了在A和B满足一定扰动条件时, 系统Ax+ B*y=b, Bx=d的最小二乘解的扰动分析.

关键词: 广义 B-D 逆, L-零矩阵, 扰动分析, 正交投影, 广义 B-D 逆, L-零矩阵, 扰动分析, 正交投影

Abstract: Let L be a subspace of Fn and PL be the orthogonal projection of Fn onto L, where F=C or R. Let A be an n×n matrix. In this paper,we will give the perturbation analysis of the generalized Bott-Duffin inverse A(L)(+)=PL(APL+I-PL)+ when A and L have small perturbation. Using this result, we establish a perturbation analysis to the least squares solution of the system Ax+ B*y=b, Bx=d under certain small perturbation of A and B.

Key words: L-zero matrix, perturbation analysis, orthogonal projection, generalized B-D inverse, L-zero matrix, perturbation analysis, orthogonal projection

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