Improved error bound for multivariate Chebyshev polynomial interpolation
Provides a sharper theoretical guarantee for a widely used numerical method, benefiting practitioners in scientific computing and approximation theory.
The paper presents an improved error bound for tensorized Chebyshev polynomial interpolation, significantly tightening existing results for high-dimensional applications.
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.