Faculté des sciences

Barycentric rational interpolation at quasi-equidistant nodes

Hormann, Kai ; Klein, Georges ; De Marchi, Stefano

In: Dolomites Research Notes on Approximation, 2012, vol. 5, p. 1-6

A collection of recent papers reveals that linear barycentric rational interpolation with the weights suggested by Floater and Hormann is a good choice for approximating smooth functions, especially when the interpolation nodes are equidistant. In the latter setting, the Lebesgue constant of this rational interpolation process is known to grow only logarithmically with the number of nodes. But... Plus

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    Summary
    A collection of recent papers reveals that linear barycentric rational interpolation with the weights suggested by Floater and Hormann is a good choice for approximating smooth functions, especially when the interpolation nodes are equidistant. In the latter setting, the Lebesgue constant of this rational interpolation process is known to grow only logarithmically with the number of nodes. But since practical applications not always allow to get precisely equidistant samples, we relax this condition in this paper and study the Floater–Hormann family of rational interpolants at distributions of nodes which are only almost equidistant. In particular, we show that the corresponding Lebesgue constants still grow logarithmically, albeit with a larger constant than in the case of equidistant nodes.