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2021 Condition Numbers for a Linear Function of the Solution to the Constrained and Weighted Least Squares Problem and Their Statistical Estimation
Mahvish Samar
Taiwanese J. Math. Advance Publication 1-25 (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.

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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. Advance Publication 1 - 25, 2021. https://doi.org/10.11650/tjm/201202

Information

Published: 2021
First available in Project Euclid: 10 December 2020

Digital Object Identifier: 10.11650/tjm/201202

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

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

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