The stability of barycentric interpolation at the Chebyshev points of the second kind

Abstract

We present a new analysis of the stability of the first and second barycentric formulae for interpolation at the Chebyshev points of the second kind. Our theory shows that the second formula is more stable than previously thought and our experiments confirm its stability in practice. % OLD: We also explain that the first barycentric formula has accuracy problems which are not properly taken into account in the current literature. We also extend our current understanding regarding the accuracy problems of the first barycentric formula.