The main objective of this paper is to construct an approximant, with cubic precision and quartic approximation order, which interpolates functional values and first order derivatives on a set of scattered data. This approximant is a combination of six-point Shepard basis functions with rational interpolants based on six-tuples of nodes. The numerical results show the efficiency and the accuracy of the proposed method, which is implemented by a fast algorithm that makes it useful in several domains of application.
Rational Hermite interpolation on six-tuples and scattered data
Dell'Accio F.
;Di Tommaso F.;
2020
Abstract
The main objective of this paper is to construct an approximant, with cubic precision and quartic approximation order, which interpolates functional values and first order derivatives on a set of scattered data. This approximant is a combination of six-point Shepard basis functions with rational interpolants based on six-tuples of nodes. The numerical results show the efficiency and the accuracy of the proposed method, which is implemented by a fast algorithm that makes it useful in several domains of application.File in questo prodotto:
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