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