Computational Experiments on the Tikhonov Regularization of the Total Least Squares Problem
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004.852:519.654 (1)
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Matematică computațională. Analiză numerică. Programarea calculatoarelor (123)
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SALAHI, Maziar, ZAREAMOGHADDAM, Hossein. Computational Experiments on the Tikhonov Regularization of the Total Least Squares Problem. In: Computer Science Journal of Moldova, 2009, nr. 1(49), pp. 14-25. ISSN 1561-4042.
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Computer Science Journal of Moldova
Numărul 1(49) / 2009 / ISSN 1561-4042 /ISSNe 2587-4330

Computational Experiments on the Tikhonov Regularization of the Total Least Squares Problem
CZU: 004.852:519.654

Pag. 14-25

Salahi Maziar, Zareamoghaddam Hossein
 
University of Guilan
 
Disponibil în IBN: 2 decembrie 2013


Rezumat

In this paper we consider finding meaningful solutions of illconditioned overdetermined linear systems Ax ¼ 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 ¯nd 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.

Cuvinte-cheie
Linear systems, Total least squares, Tikhonov regularization, Newton method,

Bisection method