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barycentric interpolation

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Stefano De Marchi
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In this work, we extend the so-called mapped bases or fake nodes approach to the barycentric rational interpolation of Floater-Hormann and to AAA ap-proximants. More precisely, we focus on the reconstruction of discontinuous functions by the S-Gibbs algorithm introduced in [12]. Numerical tests show that it yields an accurate approximation of discontinuous functions.
Stefano De Marchi
added a research item
It is well known that the classical polynomial interpolation gives bad approximation if the nodes are equispaced. A valid alternative is the family of barycentric rational interpolants introduced by Berrut in [4], analyzed in terms of stability by Berrut and Mittelmann in [5] and their extension done by Floater and Hormann in [8]. In this paper firstly we extend them to the trigonometric case, then as in the Floater-Hormann classical interpolant, we study the growth of the Lebesgue constant on equally spaced points. We show that the growth is logarithmic providing a stable interpolation operator.
Stefano De Marchi
added 2 research items
We discuss sampling (interpolation) by translates of sinc functions for data restricted to a finite interval. We indicate how the Floater–Hormann (cf. [8]) of the Berrut normalization (cf. [2]), in the case of equally spaced nodes, can be regarded as a sampling operator with improved approximation properties that remains numerically stable. We provide a compact formula for the denominator of the Floater–Hormann operator. Finally we use this compact formula to compute, for the case of the Berrut operator, the asymptotics of the associated quadrature weights.