We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the combination coefficients being incomplete Taylor expansions of the interpolated function at the interpolation points. The basis functions have the following features: (i) depend on the geodesic distance; (ii) are orthonormal with respect to the point-evaluation functionals; and (iii) have all derivatives equal zero up to a certain order at the interpolation points. Moreover, the construction of such interpolants, which belong to the class of partition of unity methods, takes advantage of not requiring any solution of linear systems.

Hermite-Birkhoff interpolation on arbitrarily distributed data on the sphere and other manifolds

ALLASIA, Giampietro;CAVORETTO, Roberto;DE ROSSI, Alessandra
2016-01-01

Abstract

We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the combination coefficients being incomplete Taylor expansions of the interpolated function at the interpolation points. The basis functions have the following features: (i) depend on the geodesic distance; (ii) are orthonormal with respect to the point-evaluation functionals; and (iii) have all derivatives equal zero up to a certain order at the interpolation points. Moreover, the construction of such interpolants, which belong to the class of partition of unity methods, takes advantage of not requiring any solution of linear systems.
2016
NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA-2016): Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”
AIP Publishing
AIP Conf. Proc.
1776
070004-1
070004-4
978-0-7354-1438-9
https://arxiv.org/pdf/1610.07048v1.pdf
Allasia, Giampietro; Cavoretto, Roberto; De Rossi, Alessandra
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1619535
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