Numerical differentiation on scattered data through multivariate polynomial interpolation
Numerical Analysis
2021-05-21 v2 Numerical Analysis
Abstract
We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor's formula monomial basis. Error bounds for the approximation of partial derivatives of any order compatible with the function regularity are provided, as well as sensitivity estimates to functional perturbations, in terms of the inverse Vandermonde coefficients that are active in the differentiation process. Several numerical tests are presented showing the accuracy of the approximation.
Cite
@article{arxiv.2105.09262,
title = {Numerical differentiation on scattered data through multivariate polynomial interpolation},
author = {Francesco Dell'Accio and F. Di Tommaso and N. Siar and M. Vianello},
journal= {arXiv preprint arXiv:2105.09262},
year = {2021}
}
Comments
20 pages, 14 Figure