A CONTRIBUTION TO THE CONDITIONING OF THE MIXED LEAST-SQUARES SCALED TOTAL LEAST-SQUARES PROBLEM

被引：0

作者：

Meng, Lingsheng ^{[1
]}

机构：

[1] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Peoples R China

来源：

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2022年 / 55卷

关键词：

mixed least-squares scaled total least-squares; condition numbers; mixed least-squares total least-squares;

D O I：

10.1553/etna_vol55s618

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new closed formula for first-order perturbation estimates for the solution of the mixed least-squares scaled total least-squares (MLSSTLS) problem is presented. It is mathematically equivalent to the one by [Zhang and Wang, Numer. Algorithms, 89 (2022), pp. 1223-1246]. With this formula, new closed formulas for the relative normwise, mixed, and componentwise condition numbers of the MLSSTLS problem are derived. Compact forms and upper bounds for the relative normwise condition number are also given in order to obtain economic storage and efficient computations.

引用

页码：618 / 626

页数：9

共 27 条

[1] A CONTRIBUTION TO THE CONDITIONING OF THE MIXED LEAST-SQUARES SCALED TOTAL LEAST-SQUARES PROBLEM
Meng L.
Electronic Transactions on Numerical Analysis, 2021, 55 : 618 - 626
[2] A CONTRIBUTION TO THE CONDITIONING OF THE TOTAL LEAST-SQUARES PROBLEM
Baboulin, Marc
Gratton, Serge
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2011, 32 (03) : 685 - 699
[3] Perturbation analysis and condition numbers of mixed least squares-scaled total least squares problem
Zhang, Pingping
Wang, Qun
NUMERICAL ALGORITHMS, 2022, 89 (03) : 1223 - 1246
[4] Perturbation analysis and condition numbers of mixed least squares-scaled total least squares problem
Pingping Zhang
Qun Wang
Numerical Algorithms, 2022, 89 : 1223 - 1246
[5] Perturbation analysis for mixed least squares-total least squares problems
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[6] An Analysis of the Mixed Least Squares-Total Least Squares Problems
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[7] SENSITIVITY AND CONDITIONING OF THE TRUNCATED TOTAL LEAST SQUARES SOLUTION
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[8] A contribution to perturbation analysis for total least squares problems
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NUMERICAL ALGORITHMS, 2017, 75 (02) : 381 - 395
[9] MODIFYING THE QR-DECOMPOSITION TO CONSTRAINED AND WEIGHTED LINEAR LEAST-SQUARES
GULLIKSSON, M
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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1992, 13 (04) : 1298 - 1313
[10] Structured conditioning theory for the total least squares problem with linear equality constraint and their estimation
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AIMS MATHEMATICS, 2023, 8 (05): : 11350 - 11372

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