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Numerische Mathematik

, Volume 136, Issue 1, pp 287–313 | Cite as

The stability of extended Floater–Hormann interpolants

  • André Pierro de Camargo
  • Walter F. MascarenhasEmail author
Article

Abstract

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.

Mathematics Subject Classification

65D05 65G30 41A20 

Supplementary material

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • André Pierro de Camargo
    • 1
  • Walter F. Mascarenhas
    • 2
    Email author
  1. 1.Centro de Matemática, Computação e CogniçãoUniversidade Federal do ABC UFABC, Rua Santa AdéliaSanto AndréBrazil
  2. 2.Instituto de Matemática e EstatísticaUniversidade de São Paulo, Cidade UniversitáriaSão PauloBrazil

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