Computational Experiments on the Tikhonov Regularization of the Total Least Squares Problem

Abstract

In this paper we consider finding meaningful solutions of ill-conditioned overdetermined linear systems Ax≈b, where A and b are both contaminated by noise. This kind of problems frequently arise in discretization of certain integral equations. One of the most popular approaches to find meaningful solutions of such systems is the so called total least squares problem. First we introduce this approach and then present three numerical algorithms to solve the resulting fractional minimization problem. In spite of the fact that the fractional minimization problem is not necessarily a convex problem, on all test problems we can get the global optimal solution. Extensive numerical experiments are reported to demonstrate the practical performance of the presented algorithms.

Keywords

• Linear systems
• Total least squares
• Tikhonov regularization
• Newton method
• Bisection method