Some Sharp Error Bounds for Multivariate Linear Interpolation and Extrapolation
Numerical Analysis
2022-09-27 v1 Numerical Analysis
Abstract
We study in this paper the function approximation error of linear interpolation and extrapolation. Several upper bounds are presented along with the conditions under which they are sharp. All results are under the assumptions that the function has Lipschitz continuous gradient and is interpolated on an affinely independent sample set. Errors for quadratic functions and errors of bivariate linear extrapolation are analyzed in depth.
Cite
@article{arxiv.2209.12606,
title = {Some Sharp Error Bounds for Multivariate Linear Interpolation and Extrapolation},
author = {Liyuan Cao and Zaiwen Wen and Ya-xiang Yuan},
journal= {arXiv preprint arXiv:2209.12606},
year = {2022}
}
Comments
18 pages, 3 figures