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.
Approximation order
Hermite interpolation
Rational interpolant
Scattered data
Shepard methods
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/306293
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