Condition numbers of multidimensional mixed least squares-total least squares problems

被引：4
作者：
Liu, Qiaohua [1 ]
Li, Chuge [1 ]
Wei, Yimin [2 ,3 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[3] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2022年 / 178卷
基金：
中国国家自然科学基金;
关键词：
Multidimensional mixed least squares-total; least squares problem; Weighted TLS problem; Condition number; AX approximate to B; PERTURBATION ANALYSIS; TO-B; COMPONENTWISE; COLUMNS;
D O I：
10.1016/j.apnum.2022.03.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper considers the multidimensional mixed least squares-total least squares (MTLS) problem which arises in the regression model, signal processing and the problem of space coordinate transformation. Firstly, the MTLS problem is proved to be equivalent to a weighted total least squares problem in the limit sense. Then, the perturbation analysis and explicit normwise, mixed and componentwise condition number formulae for the MTLS problem are presented. Tight and computable upper bounds for these condition numbers are also given. The results include the ones for the single-right-hand-side MTLS as special cases. Finally in the numerical experiments, the tightness of condition numbers and upper bounds in evaluating the forward errors is also shown. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：52 / 68
页数：17
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