20.500.12556/RUP-7734 High order parametric polynomial approximation of quadrics in R [sup] d Parametrična polinomska aproksimacija kvadrik v R [na] d z visokim redom aproksimacije In this paper an approximation of implicitly defined quadrics in ▫${\mathbb R}^d$▫ by parametric polynomial hypersurfaces is considered. The construction of the approximants provides the polynomial hypersurface in a closed form, and it is based on the minimization of the error term arising from the implicit equation of a quadric. It is shown that this approach also minimizes the normal distance between the quadric and the polynomial hypersurface. Furthermore, the asymptotic analysis confirms that the distance decreases at least exponentially as the polynomial degree grows. Numerical experiments for spatial quadrics illustrate the obtained theoretical results. V članku je obravnavana aproksimacija implicitno podatih kvadrik v ▫${\mathbb R}^d$▫ s parametričnimi polinomskimi hiperploskvami. Konstrukcija temelji na minimizaciji napake, ki sledi iz implicitne enačbe kvadrike, aproksimant pa je podan v zaključeni obliki. Obravnavan pristop prav tako minimizira normalno razdaljo med kvadriko in polinomsko hiperploskvijo. Asimptotična analiza pove,da razdalja pada vsaj eksponentno z rastočo stopnjo polinoma. Numerični primeri za prostorske kvadrike potrjujejo dobljene teoretične rezultate. mathematics quadric hypersurface conic section polynomial approximation approximation order normal distance matematika kvadrika stožnica polinomska aproksimacija red aproksimacije normalna razdalja true true false Angleški jezik Slovenski jezik Delo ni kategorizirano 2016-04-08 16:47:08 2017-04-03 08:11:48 2024-03-01 13:33:25 0000-00-00 00:00:00 2012 0 0 str. 318-332 iss. 1 Vol. 388 2012 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0022-247X 519.65 3081231 16069721 http://dx.doi.org/10.1016/j.jmaa.2011.10.044 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=7734 Inštitut Andrej Marušič 0 0 0