THE EXACT CONDITION NUMBER OF THE TRUNCATED SINGULAR VALUE SOLUTION OF A LINEAR ILL-POSED PROBLEM

被引：8

作者：

Bergou, El Houcine ^{[1
]}

Gratton, Serge ^{[1
]}

Tshimanga, Jean ^{[1
]}

机构：

[1] CERFACS, F-31057 Toulouse, France

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2014年 / 35卷 / 03期

关键词：

truncated singular value decomposition; condition number; Frechet derivative; least squares solution; perturbation theory;

D O I：

10.1137/120869286

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main result of this paper is the formulation of an explicit expression for the condition number of the truncated least squares solution of Ax = b. This expression is given in terms of the singular values of A and the Fourier coefficients of b. The result is derived using the notion of the Frechet derivative together with the product norm on the data [A, b] and the 2-norm on the solution. Numerical experiments are given to confirm our results by comparing them to those obtained by means of a finite difference approach.

引用

页码：1073 / 1085

页数：13

共 14 条

[1]

[Anonymous], 1985, Matrix Analysis

[2]

Bjorck A, 1996, NUMERICAL METHODS L

[3]

Golub G. H., 1996, MATRIX COMPUTATIONS

[4] On the condition number of linear least squares problems in a weighted Frobenius norm [J].