A note on the condition number of the scaled total least squares problem

TL;DR

This paper derives explicit and simplified expressions for the normwise condition number of the scaled total least squares problem, introduces estimation methods, and demonstrates their effectiveness through numerical experiments.

Contribution

It provides new explicit formulas and estimation techniques for the condition number of scaled total least squares problems, with computational advantages.

Findings

New explicit expressions for the condition number.

Three methods for estimating the condition number.

Numerical experiments confirm the effectiveness of the proposed results.

Abstract

In this paper, we consider the explicit expressions of the normwise condition number for the scaled total least squares problem. Some techniques are introduced to simplify the expression of the condition number, and some new results are derived. Based on these new results, new expressions of the condition number for the total least squares problem can be deduced as a special case. New forms of the condition number enjoy some storage and computational advantages. We also proposed three different methods to estimate the condition number. Some numerical experiments are carried out to illustrate the effectiveness of our results.