Two and Three Dimensional Partition of Unity Interpolation by Product-Type Functions

Authors

Roberto Cavoretto, Department of Mathematics “G. Peano”, University of Torino, Via Carlo Alberto 10, 10123 Torino, ItalyFollow

Author Country (or Countries)

Italy

Abstract

In this paper we analyze the behavior of product-type radial basis functions (RBFs) and splines, which are used in a partition of unity interpolation scheme as local approximants. In particular, we deal with the case of bivariate and trivariate interpolation on a relatively large number of scattered data points. Thus, we propose the local use of compactly supported RBF and spline interpolants, which take advantage of being expressible in the multivariate setting as a product of univariate functions. Numerical experiments show good accuracy and stability of the partition of unity method combined with these product-type interpolants, comparing it with the one obtained by replacing compactly supported RBFs and splines with Gaussians.

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/090101

Recommended Citation

Cavoretto, Roberto (2023) "Two and Three Dimensional Partition of Unity Interpolation by Product-Type Functions," Applied Mathematics & Information Sciences: Vol. 09: Iss. 1, Article 8.
DOI: http://dx.doi.org/10.12785/amis/090101
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss1/8