High order parametric polynomial approximation of quadrics in Rd

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Jaklic, Gasper^1,2,3  Kozak, Jernej^2,3  Krajnc, Marjeta^2,3  Vitrih, Vito^1,4  Zagar, Emil^2,3 

[1] Univ Primorska, PINT, Koper, Slovenia

[2] Univ Ljubljana, FMF, Ljubljana, Slovenia

[3] IMFM, Ljubljana, Slovenia

[4] Univ Primorska, FAMNIT, Koper, Slovenia

关键词: Quadric hypersurface;    Conic section;    Polynomial approximation;    Approximation order;    Normal distance;   

DOI  :  10.1016/j.jmaa.2011.10.044

来源: Elsevier

【 摘 要 】

In this paper an approximation of implicitly defined quadrics in 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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free