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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 9, Pages 1433–1443
DOI: https://doi.org/10.7868/S0044466917090149 (Mi zvmmf10609) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Generalizations of Tikhonov’s regularized method of least squares to non-Euclidean vector norms

V. V. Volkova, V. I. Erokhinb, V. V. Kakaevb, A. Yu. Onufreib

a Borisoglebsk Branch, Voronezh State University, Borisoglebsk, Russia
b Mozhaisky Military Space Academy, St. Petersburg, Russia
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DOI: https://doi.org/10.7868/S0044466917090149
Abstract: Tikhonov’s regularized method of least squares and its generalizations to non-Euclidean norms, including polyhedral, are considered. The regularized method of least squares is reduced to mathematical programming problems obtained by “instrumental” generalizations of the Tikhonov lemma on the minimal (in a certain norm) solution of a system of linear algebraic equations with respect to an unknown matrix. Further studies are needed for problems concerning the development of methods and algorithms for solving reduced mathematical programming problems in which the objective functions and admissible domains are constructed using polyhedral vector norms.
Key words: approximate system of linear algebraic equations, Tikhonov’s regularized method of least squares, non-Euclidean vector norms.
Funding agency Grant number
Russian Foundation for Basic Research 16-31-50016_мол_нр
Received: 26.05.2016
Revised: 10.10.2016
English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 9, Pages 1416–1426
DOI: https://doi.org/10.1134/S0965542517090147
Bibliographic databases:
Document Type: Article
UDC: 519.638
Language: Russian
Citation: V. V. Volkov, V. I. Erokhin, V. V. Kakaev, A. Yu. Onufrei, “Generalizations of Tikhonov’s regularized method of least squares to non-Euclidean vector norms”, Zh. Vychisl. Mat. Mat. Fiz., 57:9 (2017), 1433–1443; Comput. Math. Math. Phys., 57:9 (2017), 1416–1426
Citation in format AMSBIB
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