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
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
收藏
页码:1073 / 1085
页数:13
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