Structured condition numbers for the total least squares problem with linear equality constraint and their statistical estimation
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.
Cite
@article{arxiv.2105.08132,
title = {Structured condition numbers for the total least squares problem with linear equality constraint and their statistical estimation},
author = {Mahvish Samar},
journal= {arXiv preprint arXiv:2105.08132},
year = {2021}
}
Comments
There are servals reasons. 1) I need to add some new results in section 3 for unstructured condition number. 2) need to add new authors list. 3) we want to add more numerical example to show our results efficient and take less time. 4) We want to add the comparison in section 4