On condition numbers for least squares with quadric inequality constraint

Diao, Huaian

doi:10.1016/j.camwa.2016.12.033

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Condition Numbers Of the Tlse Problem1

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Cited by 10 publications

(2 citation statements)

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“…Note that the explicit expression of three types of condition numbers all involve the Kronecker product, which makes the storage and computation very costly. For the norm-wise condition number, the compact formula can be obtained by applying the following lemma, which is a slight revision of Lemma 2.1 in [3].…”

Section: Condition Numbers Of the Tlse Problemmentioning

confidence: 99%

The revisited total least squares problems with linear equality constraint

Liu

Jin

Yao

et al. 2020

Applied Numerical Mathematics

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Section: Condition Numbers Of the Tlse Problemmentioning

confidence: 99%

The revisited total least squares problems with linear equality constraint

Liu

Jin

Yao

et al. 2020

Applied Numerical Mathematics

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“…To remedy this drawback, we adopt a modified definition of condition number, the projected condition number, which can be used to provide a unified framework of the condition number theory and give more elaborate error analysis of the EILS problem. More researches on the normwise, mixed, and componentwise condition numbers of LS problems can be found in [1,2,9,10,14,24,25,29,44].…”

mentioning

confidence: 99%

On the Condition Number Theory of the Equality Constrained Indefinite Least Squares Problem

Wang

Yang

2018

ELA

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In this paper, within a unified framework of the condition number theory we present the explicit expression of the projected condition number of the equality constrained indefinite least squares problem. By setting specific norms and parameters, some widely used condition numbers, like the normwise, mixed and componentwise condition numbers follow as its special cases. Considering practical applications and computation, some new compact forms or upper bounds of the projected condition numbers are given to improve the computational efficiency. The new compact forms are of particular interest in calculating the exact value of the 2-norm projected condition numbers. When the equality constrained indefinite least squares problem degenerates into some specific least squares problems, our results give some new findings on the condition number theory of these specific least squares problems. Numerical experiments are given to illustrate our theoretical results.

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On condition numbers of the total least squares problem with linear equality constraint

Liu

Jia

2022

Numer Algor

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On condition numbers for least squares with quadric inequality constraint

Cited by 10 publications

References 18 publications

The revisited total least squares problems with linear equality constraint

The revisited total least squares problems with linear equality constraint

On the Condition Number Theory of the Equality Constrained Indefinite Least Squares Problem

On condition numbers of the total least squares problem with linear equality constraint

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