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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, Volume 9, Issue 1, Pages 53–63
DOI: https://doi.org/10.21638/spbu01.2022.106 (Mi vspua41) 		 
MATHEMATICS

Representations of continuous piecewise affine functions

V. N. Malozemova, G. Sh. Tamasyanab

a St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
b Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences, 61, Bolshoy pr. V.O., St Petersburg, 199178, Russian Federation
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DOI: https://doi.org/10.21638/spbu01.2022.106
Abstract: Continuous piecewise affine functions are widely used in computational mathematics. In one-dimensional case such functions are called broken lines. The article analyzes the analytical representations of broken lines in the forms accepted in the theory of polynomial splines as well as in the form of the difference of the maxima of two finite families of affine functions. The connection between these representation is being determined.
Keywords: piecewise affine function, broken line, analytical representations of broken lines, difference of convex functions.
Funding agency Grant number
Russian Science Foundation 20-71-10032
The results of Section 7 were obtained in the Institute of Problems of Mechanical Engineering, Russian Academy of Sciences with the support of the Russian Science Foundation (project No. 20-71-10032).
Received: 10.06.2021
Revised: 26.08.2021
Accepted: 02.09.2021
English version:
Vestnik St. Petersburg University, Mathematics, 2022, Volume 9, Issue 1, Pages 39–47
DOI: https://doi.org/10.1134/S1063454122010083
Document Type: Article
UDC: 519.853
MSC: 65D15, 65D05
Language: Russian
Citation: V. N. Malozemov, G. Sh. Tamasyan, “Representations of continuous piecewise affine functions”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9:1 (2022), 53–63; Vestn. St. Petersbg. Univ., Math., 9:1 (2022), 39–47
Citation in format AMSBIB
\Bibitem{MalTam22}
\by V.~N.~Malozemov, G.~Sh.~Tamasyan
\paper Representations of continuous piecewise affine functions
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2022
\vol 9
\issue 1
\pages 53--63
\mathnet{http://mi.mathnet.ru/vspua41}
\crossref{https://doi.org/10.21638/spbu01.2022.106}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2022
\vol 9
\issue 1
\pages 39--47
\crossref{https://doi.org/10.1134/S1063454122010083}
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