In this paper, we construct and analyse C1 quartic interpolating splines on type-1 triangulations, approximating regularly distributed data. This is achieved by defining the associated Bernstein-Bézier coefficients from point values of the function to be approximated in such a way that C1 regularity is obtained for enough regular functions as well as the optimal order of approximation. We construct such interpolating splines by combining a quasi-interpolating spline with one step of an interpolatory subdivision scheme. Numerical tests confirming the theoretical results are provided.

C1-Quartic Butterfly-Spline Interpolation on Type-1 Triangulations

Dagnino, Catterina;Remogna, Sara
2021

Abstract

In this paper, we construct and analyse C1 quartic interpolating splines on type-1 triangulations, approximating regularly distributed data. This is achieved by defining the associated Bernstein-Bézier coefficients from point values of the function to be approximated in such a way that C1 regularity is obtained for enough regular functions as well as the optimal order of approximation. We construct such interpolating splines by combining a quasi-interpolating spline with one step of an interpolatory subdivision scheme. Numerical tests confirming the theoretical results are provided.
Approximation Theory 16
Nashville, USA
May 19 — 22, 2019
Approximation Theory XVI
Springer, Cham
336
11
26
978-3-030-57463-5
978-3-030-57464-2
Spline approximation, Bernstein-Bézier form, Type-1 triangulation
Barrera, Domingo; Conti, Costanza; Dagnino, Catterina; Ibáñez, María José; Remogna, Sara
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1788060
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