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Mathematics > Numerical Analysis

arXiv:2209.12606 (math)
[Submitted on 26 Sep 2022]

Title:Some Sharp Error Bounds for Multivariate Linear Interpolation and Extrapolation

Authors:Liyuan Cao, Zaiwen Wen, Ya-xiang Yuan
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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.
Comments: 18 pages, 3 figures
Subjects: Numerical Analysis (math.NA)
MSC classes: 41A05, 41A10, 41A80, 46N10
Cite as: arXiv:2209.12606 [math.NA]
  (or arXiv:2209.12606v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2209.12606

Submission history

From: Liyuan Cao [view email]
[v1] Mon, 26 Sep 2022 11:53:31 UTC (46 KB)
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