Mixed and componentwise condition numbers for a linear function of the solution of the total least squares problem

Abstract

In this paper, we consider the mixed and componentwise condition numbers for a linear function Lx of the solution to the total least squares (TLS) problem. We derive the explicit expressions of the mixed and componentwise condition numbers through the dual techniques under both unstructured and structured componentwise perturbations. The sharp upper bounds for condition numbers are obtained. An efficient condition estimation algorithm is proposed, which can be integrated into the iterative method for solving large scale TLS problems. Moreover, the new derived condition number expressions can recover the previous results on the condition analysis for the TLS problem when L=In. Numerical experiments show the effectiveness of the introduced condition numbers and condition estimation algorithm.