Work

Some Sharp Error Bounds for Multivariate Linear Interpolation and Extrapolation

Year: 2022

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2209.12606

Authors: Cao, Liyuan, Wen, Zaiwen, Yuan, Ya-xiang

Institutions: Peking University, Chinese Academy of Sciences, Academy of Mathematics and Systems Science, State Key Laboratory of Scientific and Engineering Computing

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G2030148605

OpenAlex ID: W4297433460

Cites:

Cited by: 1

Related to: 10