This article is cited in 6 papers

Solution of the linear regression problem using matrix correction methods in the $l_1$ metric

V. A. Gorelik^a, O. S. Trembacheva (Barkalova)<sup>b

a</sup> Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
^b Moscow State Pedagogical University, ul. Malaya Pirogovskaya 1, Moscow, 119882, Russia

Abstract: The linear regression problem is considered as an improper interpolation problem. The metric $l_1$ is used to correct (approximate) all the initial data. A probabilistic justification of this metric in the case of the exponential noise distribution is given. The original improper interpolation problem is reduced to a set of a finite number of linear programming problems. The corresponding computational algorithms are implemented in MATLAB.

Key words: data processing, regression problem, matrix correction, maximum likelihood method, exponential distribution.

UDC: 519.61

Received: 12.05.2015

DOI: 10.7868/S0044466916020083

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:2, 200–205

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