Some Sharp Error Bounds for Multivariate Linear Interpolation and Extrapolation
- Resource Type
- Working Paper
- Authors
- Cao, Liyuan; Wen, Zaiwen; Yuan, Ya-xiang
- Source
- Subject
- Mathematics - Numerical Analysis
41A05, 41A10, 41A80, 46N10
- Language
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.
Comment: 18 pages, 3 figures