Cardinal interpolation: A bivariate polynomial example
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.
scientific article; zbMATH DE number 4022456