Volume 23, Issue 5
On Stable Perturbations of the Stiffly Weighted Pseudoinverse and Weighted Least Squares Problem

Mu-Sheng Wei

J. Comp. Math., 23 (2005), pp. 527-536.

Published online: 2005-10

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  • Abstract

In this paper we study perturbations of the stiffly weighted pseudoinverse $ (W^{1\over 2}A)^†W^{1\over 2}$ and the related stiffly weighted least squares problem, where both the matrices $A$ and $W$ are given with $W$ positive diagonal and severely stiff. We show that the perturbations to the stiffly weighted pseudoinverse and the related stiffly weighted least squares problem are stable, if and only if the perturbed matrices $\widehat A=A+\delta A$ satisfy several row rank preserving conditions.  

  • Keywords

Stiffly, Weighted pseudoinverse, Weighted least squares, Perturbation, Stability.

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@Article{JCM-23-527, author = {}, title = {On Stable Perturbations of the Stiffly Weighted Pseudoinverse and Weighted Least Squares Problem}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {5}, pages = {527--536}, abstract = {

In this paper we study perturbations of the stiffly weighted pseudoinverse $ (W^{1\over 2}A)^†W^{1\over 2}$ and the related stiffly weighted least squares problem, where both the matrices $A$ and $W$ are given with $W$ positive diagonal and severely stiff. We show that the perturbations to the stiffly weighted pseudoinverse and the related stiffly weighted least squares problem are stable, if and only if the perturbed matrices $\widehat A=A+\delta A$ satisfy several row rank preserving conditions.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8837.html} }
TY - JOUR T1 - On Stable Perturbations of the Stiffly Weighted Pseudoinverse and Weighted Least Squares Problem JO - Journal of Computational Mathematics VL - 5 SP - 527 EP - 536 PY - 2005 DA - 2005/10 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8837.html KW - Stiffly, Weighted pseudoinverse, Weighted least squares, Perturbation, Stability. AB -

In this paper we study perturbations of the stiffly weighted pseudoinverse $ (W^{1\over 2}A)^†W^{1\over 2}$ and the related stiffly weighted least squares problem, where both the matrices $A$ and $W$ are given with $W$ positive diagonal and severely stiff. We show that the perturbations to the stiffly weighted pseudoinverse and the related stiffly weighted least squares problem are stable, if and only if the perturbed matrices $\widehat A=A+\delta A$ satisfy several row rank preserving conditions.  

Mu-Sheng Wei. (1970). On Stable Perturbations of the Stiffly Weighted Pseudoinverse and Weighted Least Squares Problem. Journal of Computational Mathematics. 23 (5). 527-536. doi:
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