Cardinal interpolation: A bivariate polynomial example
type: Item
instance of: scholarly article
title: Cardinal interpolation: A bivariate polynomial example
zbMATH Open document ID: 0628.65006
DOI: 10.1016/0167-8396(86)90006-3
author: K. L. Rescorla
published in: Computer Aided Geometric Design
publication date: 1986-01-01T00:00:00Z
review text: The author gives a result about the resolution of the general interpolation problem over a linear space to prove explicit formulas for the cardinal basis of the space. As an example of this technique, the cardinal form of a bivariate degree-nine polynomial interpolating to function and derivative values through order four at various points in a triangle is derived. The polynomial interpolant over an arbitrary triangulated domain in \({\mathbb{R}}^ 2\) has the following properties: The required data are \(C^ 4\), the smoothness is \(C^ 2\), the precision set consists of all polynomials of degree less than or equal nine, and the interpolant is a degree-nine piecewise polynomial in cardinal form.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 4022456
zbMATH Keywords: polynomial interpolation
zbMATH Keywords: bivariate interpolation
zbMATH Keywords: cardinal form
reviewed by: Antonio López-Carmona
MaRDI profile type: Publication
full work available at URL: 0167-8396(86)90006-3
OpenAlex ID: W2062572304
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description: scientific article; zbMATH DE number 4022456