**Authors:** Maziar Salahi, Hossein Zareamoghaddam

**Keywords:** Linear systems, Total least squares, Tikhonov regularization, Newton method, Bisection method

### 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.

Department of Mathematics,

Faculty of Sciences,

University of Guilan,

Rasht, Namjoo Street, Guilan, P.O.Box 1914

E-mail: ,

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