Structured condition numbers for the total least squares problem with linear equality constraint and their statistical estimation

TL;DR

This paper derives explicit mixed and componentwise condition numbers for the constrained total least squares problem, providing statistical estimation methods and numerical validation for their accuracy and reliability.

Contribution

It introduces explicit formulas for structured and unstructured condition numbers in TLSE problems and applies statistical estimation for practical computation.

Findings

Explicit formulas for mixed and componentwise condition numbers.

Statistical estimation method for condition numbers with high reliability.

Numerical experiments validating the theoretical results.

Abstract

In this paper, we derive the mixed and componentwise condition numbers for a linear function of the solution to the total least squares with linear equality constraint (TLSE) problem. The explicit expressions of the mixed and componentwise condition numbers by dual techniques under both unstructured and structured componentwise perturbations is considered. With the intermediate result, i.e. we can recover the both unstructured and structured condition number for the TLS problem. We choose the small-sample statistical condition estimation method to estimate both unstructured and structured condition numbers with high reliability. Numerical experiments are provided to illustrate the obtained results.