The effects of rounding errors in the nodes on barycentric interpolation

We analyze the effects of rounding errors in the nodes on barycentric interpolation. These errors are particularly relevant for the first barycentric formula with the Chebyshev points of the second kind. Here, we propose a method for reducing them.Comment: We fixed a few grammar errors and a minor mistake in Theorem 8: 2n + 5 was replaced by 2n +

On the backward stability of the second barycentric formula for interpolation

We present a new stability analysis for the second barycentric formula for interpolation, showing that this formula is backward stable when the relevant Lebesgue constant is small

Moore: Interval Arithmetic in C++20

This article presents the Moore library for interval arithmetic in C++20. It gives examples of how the library can be used, and explains the basic principles underlying its design.Comment: arXiv admin note: text overlap with arXiv:1611.09567

The stability of extended Floater-Hormann interpolants

We present a new analysis of the stability of extended Floater-Hormann interpolants, in which both noisy data and rounding errors are considered. Contrary to what is claimed in the current literature, we show that the Lebesgue constant of these interpolants can grow exponentially with the parameters that define them, and we emphasize the importance of using the proper interpretation of the Lebesgue constant in order to estimate correctly the effects of noise and rounding errors. We also present a simple condition that implies the backward instability of the barycentric formula used to implement extended interpolants. Our experiments show that extended interpolants mentioned in the literature satisfy this condition and, therefore, the formula used to implement them is not backward stable. Finally, we explain that the extrapolation step is a significant source of numerical instability for extended interpolants based on extrapolation.Comment: In this version we present a new figure illustrating the practical relevance of the cases considered in the article, and changed the wording of several sentences. There were no changes in the mathematical content of the articl