OPTIMAL BACKWARD PERTURBATION BOUNDS FOR THE LINEAR LEAST-SQUARES PROBLEM

被引：41

作者：

WALDEN, B ^{[1
]}

KARLSON, R ^{[1
]}

SUN, JG ^{[1
]}

机构：

[1] UMEA UNIV,INST INFORMAT PROC,S-90187 UMEA,SWEDEN

来源：

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 1995年 / 2卷 / 03期

关键词：

LINEAR LEAST SQUARES; BACKWARD PERTURBATIONS;

D O I：

10.1002/nla.1680020308

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A be an m x n matrix, b be an m-vector, and ($) over tilde x: be a purported solution to the problem of minimizing \\b - Ax\\(2). We consider the following open problem: find the smallest perturbation E of A such that the vector ($) over tilde x exactly minimizes \\b - (A + E)x\\(2). This problem is completely solved when E is measured in the Frobenius norm. When using the spectral norm of E, upper and lower bounds are given, and the optimum is found under certain conditions.

引用

页码：271 / 286

页数：16