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Title:High order parametric polynomial approximation of quadrics in R [sup] d
Authors:ID Jaklič, Gašper (Author)
ID Kozak, Jernej (Author)
ID Knez, Marjetka (Author)
ID Vitrih, Vito (Author)
ID Žagar, Emil (Author)
Files:URL http://dx.doi.org/10.1016/j.jmaa.2011.10.044
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
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.
Keywords:mathematics, quadric hypersurface, conic section, polynomial approximation, approximation order, normal distance
Year of publishing:2012
Number of pages:str. 318-332
Numbering:Vol. 388, iss. 1
PID:20.500.12556/RUP-7734 This link opens in a new window
ISSN:0022-247X
UDC:519.65
COBISS.SI-ID:16069721 This link opens in a new window
Publication date in RUP:03.04.2017
Views:2727
Downloads:34
Metadata:XML DC-XML DC-RDF
:
JAKLIČ, Gašper, KOZAK, Jernej, KNEZ, Marjetka, VITRIH, Vito and ŽAGAR, Emil, 2012, High order parametric polynomial approximation of quadrics in R [sup] d. [online]. 2012. Vol. 388, no. 1, p. 318–332. [Accessed 5 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.jmaa.2011.10.044
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Secondary language

Language:Slovenian
Title:Parametrična polinomska aproksimacija kvadrik v R [na] d z visokim redom aproksimacije
Abstract:V članku je obravnavana aproksimacija implicitno podatih kvadrik v Rd 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.
Keywords:matematika, kvadrika, stožnica, polinomska aproksimacija, red aproksimacije, normalna razdalja


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