Improved error bound for multivariate Chebyshev polynomial interpolation

TL;DR

This paper presents a significantly improved error bound for tensorized Chebyshev polynomial interpolation, enhancing its efficiency and reliability in high-dimensional applications.

Contribution

The authors derive a sharper error bound for multivariate Chebyshev interpolation, advancing the theoretical understanding and practical utility of the method.

Findings

New error bound is tighter than previous results

Enhanced efficiency for high-dimensional interpolation tasks

Supports more reliable implementation of Chebyshev methods

Abstract

Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For efficiency, a sharp error bound is essential, in particular for high-dimensional applications. For tensorized Chebyshev interpolation, we present an error bound that improves existing results significantly.