Explicit multivariate approximations from cell-average data
Numerical Analysis
2021-12-21 v1 Numerical Analysis
Abstract
Given gridded cell-average data of a smooth multivariate function, we present a constructive explicit procedure for generating a high-order global approximation of the function. One contribution is the derivation of high order approximations to point-values of the function directly from the cell-average data. The second contribution is the development of univariate B-spline based high order quasi-interpolation operators using cell-average data. Multivariate spline quasi-interpolation approximation operators are obtained by tensor products of the univariate operators.
Cite
@article{arxiv.2112.10119,
title = {Explicit multivariate approximations from cell-average data},
author = {Sergio Amat and David Levin and Juan Ruiz-Alvarez and Dionisio F. Yáñez},
journal= {arXiv preprint arXiv:2112.10119},
year = {2021}
}