PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

High order parametric polynomial approximation of quadrics in R [sup] d
Gašper Jaklic, Jernej Kozak, Marjetka Krajnc, Vito Vitrih and Emil Žagar
Journal of mathematical analysis and applications Volume 388, Number 1, pp. 318-332, 2012. ISSN 0022-247X

Abstract

In this paper an approximation of implicitly defined quadrics in Rd 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.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:9257
Deposited By:Boris Horvat
Deposited On:21 February 2012