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BIT Numerical Mathematics

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01-09-2015

Shape preserving \(HC^2\) interpolatory subdivision

Authors: Davide Lettieri, Carla Manni, Francesca Pelosi, Hendrik Speleers

Published in: BIT Numerical Mathematics | Issue 3/2015

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Abstract

A subdivision procedure is developed to solve a \(C^2\) Hermite interpolation problem with the further request of preserving the shape of the initial data. We consider a specific non-stationary and non-uniform variant of the Merrien \(HC^2\) subdivision family, and we provide a data dependent strategy to select the related parameters which ensures convergence and shape preservation for any set of initial monotone and/or convex data. Each step of the proposed subdivision procedure can be regarded as the midpoint evaluation of an interpolating function—and of its first and second derivatives—in a suitable space of \(C^2\) functions of dimension \(6\) which has tension properties. The limit function of the subdivision procedure is a \(C^2\) piecewise quintic polynomial interpolant.

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The monotone decreasing case can be addressed in a similar way.

The concave case can be addressed in a similar way.

The Maple worksheets with all the computations can be found at http://www.mat.uniroma2.it/~manni/Maple_HC2.html.

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Title: Shape preserving interpolatory subdivision
Authors: Davide Lettieri
Carla Manni
Francesca Pelosi
Hendrik Speleers
Publication date: 01-09-2015
Publisher: Springer Netherlands
Published in: BIT Numerical Mathematics / Issue 3/2015
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-014-0530-0

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