Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2017; 54(2): 613-626

Online first article December 27, 2016      Printed March 1, 2017

https://doi.org/10.4134/JKMS.j160152

Copyright © The Korean Mathematical Society.

Dual regularized total least squares solution from two-parameter trust-region algorithm

Geunseop Lee

Samsung Electronics Co. Ltd

Abstract

For the overdetermined linear system, when both the data matrix and the observed data are contaminated by noise, Total Least Squares method is an appropriate approach. Since an ill-conditioned data matrix with noise causes a large perturbation in the solution, some kind of regularization technique is required to filter out such noise. In this paper, we consider a Dual regularized Total Least Squares problem. Unlike the Tikhonov regularization which constrains the size of the solution, a Dual regularized Total Least Squares problem considers two constraints; one constrains the size of the error in the data matrix, the other constrains the size of the error in the observed data. Our method derives two nonlinear equations to construct the iterative method. However, since the Jacobian matrix of two nonlinear equations is not guaranteed to be nonsingular, we adopt a trust-region based iteration method to obtain the solution.

Keywords: dual regularized total least squares method, trust region algorithm

MSC numbers: Primary 65F10, 65F22

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