Thomas Lux, Layne T. Watson, Tyler Chang

Abstract

Increases in the quantity of available data have allowed all fields of science to generate more accurate models of multivariate phenomena. Regression and interpolation become challenging when the dimension of data is large, especially while maintaining tractable computational complexity. Regression is a popular approach to solving approximation problems with high dimension; however, there are often advantages to interpolation. This paper presents a novel and insightful error bound for (piecewise) linear interpolation in arbitrary dimension and contrasts the performance of some interpolation techniques with popular regression techniques. Empirical results demonstrate the viability of interpolation for moderately high-dimensional approximation problems, and encourage broader application of interpolants to multivariate approximation in science.

People

Thomas Lux


Tyler Chang


Layne T. Watson


Publication Details

Date of publication:
November 13, 2020
Journal:
Numerical Algorithms
Page number(s):
281–313
Volume:
88
Publication note:

Thomas C. H. Lux, Layne T. Watson, Tyler H. Chang, Yili Hong, Kirk W. Cameron: Interpolation of sparse high-dimensional data. Numer. Algorithms 88(1): 281-313 (2021)