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High order parametric polynomial approximation of quadrics in R [sup] d
Gašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2012, original scientific article

Abstract: 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.
Keywords: mathematics, quadric hypersurface, conic section, polynomial approximation, approximation order, normal distance
Published in RUP: 03.04.2017; Views: 2038; Downloads: 32
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High order parametric polynomial approximation of conic sections
Gašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2013, original scientific article

Abstract: V članku je obravnavana parametrična polinomska aproksimacija stožnic, ki ohranja obliko. Pristop je osnovan na parametrični aproksimaciji implicitno definiranih ravninskih krivulj. Polinomski aproksimanti so zapisani v zaključeni obliki in ponujajo najvišji možen red aproksimacije.
Keywords: matematika, stožnica, parametrična krivulja, implicitna krivulja, aproksimacija, mathematics, conic section, parametric curve, implicit curve, approximation
Published in RUP: 03.04.2017; Views: 1920; Downloads: 82
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