Open Access
Translator Disclaimer
August, 2021 Condition Numbers for a Linear Function of the Solution to the Constrained and Weighted Least Squares Problem and Their Statistical Estimation
Mahvish Samar
Author Affiliations +
Taiwanese J. Math. 25(4): 717-741 (August, 2021). DOI: 10.11650/tjm/201202

Abstract

In this paper, we consider the condition number theory for a linear function of the solution to the constrained and weighted least squares problem. We first present two explicit expressions without Kronecker product of normwise condition number using the classical method for condition numbers. Then, we derive the explicit expression of mixed and componentwise condition numbers by the dual techniques. To estimate these condition numbers with high reliability, we choose the probabilistic spectral norm estimator and the small-sample statistical condition estimation method and devise three algorithms. Numerical experiments are provided to illustrate the obtained results.

Funding Statement

This work is supported by the National Natural Science Foundation of China (Grant No. 11771265).

Citation

Download Citation

Mahvish Samar. "Condition Numbers for a Linear Function of the Solution to the Constrained and Weighted Least Squares Problem and Their Statistical Estimation." Taiwanese J. Math. 25 (4) 717 - 741, August, 2021. https://doi.org/10.11650/tjm/201202

Information

Received: 25 September 2020; Revised: 29 November 2020; Accepted: 3 December 2020; Published: August, 2021
First available in Project Euclid: 10 December 2020

Digital Object Identifier: 10.11650/tjm/201202

Subjects:
Primary: 15A12 , 15A60 , 65F20 , 65F30 , 65F35

Keywords: componentwise condition number , constrained and weighted least squares problem , dual technique , mixed condition number , normwise condition number , probabilistic spectral norm estimator , small-sample statistical condition estimation

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

JOURNAL ARTICLE
25 PAGES


SHARE
Vol.25 • No. 4 • August, 2021
Back to Top