Improved error bound for multivariate Chebyshev polynomial interpolation

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.

Keywords: (Tensorized) Chebyshev Polynomials, Polynomial Interpolation, Error Bounds