Function approximation for building the algorithm for the rough terrain description
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2016.1.13Keywords:
function, polynomial, approximation, derivativeAbstract
The paper studies one version of the piecewise polynomial approximation using the "possible directions" method and G. Zoutendijk's method to solve the problems of describing complex functions. In particular, the problem with one quadratic constraint was presented and the methods of quadratic programming with a prior statement of the dual problems were used to solve it. To solve this problem we use an approach based on the duality theory applying a direct algorithm of the simplex method. The algorithm is presented with the goal of the further software implementation. The conclusions are made about the practical value of this research, in particular, about the possibility of expanding the tools for decision-makers for describing the affected areas of rough terrain by man-made accidents and justification of a new approach for constructing three-dimensional models of convex and concave objects.References
Vasilenko V.A. Splajn-funktsii: teorija, algoritmy, programmy / V.A. Vasilenko. — Novosibirsk: Nauka, 1983. — 218 s.
Dzjadik V.K. Vvedenie v teoriju ravnomernogo priblizhenija funktsij polinomami / V.K. Dzjadik. — M.: Nauka, 1977. — 512 s.
Popov B.A. Ravnomernoe priblizhenie splajnami / B.A. Popov. — K.: Nauk. dumka, 1989. — 272 s.
Ljuk Ju. Spetsial'nye matematicheskie funktsii i ih approksimatsii / Ju. Ljuk. — M.: Mir, 1980. — 608 s.
Zojtendejk G. Metody vozmozhnyh napravlenij / G. Zojtendejk— M.: Izd-vo inostr. lit-ry, 1963. — 178 s.
Dovhyj S.O. Systemy pidtrymky pryjnjattja rishen' na osnovi statystychno-jmovirnisnykh metodiv / S.O. Dovhyj, P.I. Bidjuk, O.M. Trofymchuk. — K.: Lohos, 2014. — 419 s.
Dovhyj S.O. Metody prohnozuvannja v systemakh pidtrymky pryjnjattja rishen' / S.O. Dovhyj, P.I. Bidjuk, O.M. Trofymchuk, O.I. Savenkov. — K.: Azymut-Ukrayina, 2011. — 608 s.
Al'berg Dzh. Teorija splajnov i ee prilozhenija / Dzh. Al'berg, E. Nil'son, Dzh. Uolsh; per. s angl. — M.: Mir, 1972. — 318 s.
Remez E.Ja. Osnovy chislennyh metodov chebyshevskogo priblizhenija / E.Ja. Remez. — K.: Nauk. dumka, 1969. — 620 s.
Boeviki zaminirovali i ugrozhajut vzorvat' v Donetskoj oblasti himzavod. [Digital source]. — http://www.62.ua/article/559907.
Boeviki ugrozhajut vzorvat' himzavod "Stirol" [Digital source]. — http://censor.net.ua/news/295664/lidery_terroristov_girkin_i_bezler_ischezli_v_neizvestnom_ napravlenii_boeviki_ugrojayut_vzorvat_himzavod.
