Interpolation of sparse high-dimensional data

被引：8

作者：

Lux, Thomas C. H. ^{[1
]}

Watson, Layne T. ^{[1
]}

Chang, Tyler H. ^{[1
]}

Hong, Yili ^{[1
]}

Cameron, Kirk ^{[1
]}

机构：

[1] Virginia Polytech Inst & State Univ VPI SU, Blacksburg, VA 24061 USA

来源：

NUMERICAL ALGORITHMS | 2021年 / 88卷 / 01期

基金：

美国国家科学基金会;

关键词：

Approximation; Regression; Interpolation; High dimension; Error bound; POLYNOMIAL INTERPOLATION; VARIANCE; FEKETE;

D O I：

10.1007/s11075-020-01040-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：281 / 313

页数：33