SENSITIVITY AND CONDITIONING OF THE TRUNCATED TOTAL LEAST SQUARES SOLUTION

被引：20

作者：

Gratton, Serge ^{[1
]}

Titley-Peloquin, David ^{[2
]}

Ilunga, Jean Tshimanga ^{[2
]}

机构：

[1] IRIT CERFACS, F-31057 Toulouse, France

[2] IRIT ENSEEIHT, F-31071 Toulouse, France

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2013年 / 34卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

truncated total least squares; condition number estimation; Frechet derivative; least squares; perturbation theory; CONDITION NUMBERS; PERTURBATION ANALYSIS; TIKHONOV REGULARIZATION; BOUNDS;

D O I：

10.1137/120895019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an explicit expression for the condition number of the truncated total least squares (TLS) solution of Ax approximate to b. This expression is obtained using the notion of the Frechet derivative. We also give upper bounds on the condition number, which are simple to compute and interpret. These results generalize those in the literature for the untruncated TLS problem. Numerical experiments demonstrate that our bounds are often a very good estimate of the condition number, and provide a significant improvement to known bounds.

引用

页码：1257 / 1276

页数：20

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