2014/09/09 by André Pierro de Camargo, de Camargo, Andre Pierro, Walter F. Mascarenhas +1
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.1409.2808
openalex publication_date 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.