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arXiv · 1601.02262

Bivariate hierarchical Hermite spline quasi--interpolation

Cesare Bracco·Carlotta Giannelli·Francesca Mazzia·Alessandra Sestini
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Abstract

Spline quasi-interpolation (QI) is a general and powerful approach for the construction of low cost and accurate approximations of a given function. In order to provide an efficient adaptive approximation scheme in the bivariate setting, we consider quasi-interpolation in hierarchical spline spaces. In particular, we study and experiment the features of the hierarchical extension of the tensor-product formulation of the Hermite BS quasi-interpolation scheme. The convergence properties of this hierarchical operator, suitably defined in terms of truncated hierarchical B-spline bases, are analyzed. A selection of numerical examples is presented to compare the performances of the hierarchical and tensor-product versions of the scheme.

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Cesare Bracco, Carlotta Giannelli, Francesca Mazzia, Alessandra Sestini. 2016-01-10. Bivariate hierarchical Hermite spline quasi--interpolation. https://doi.org/10.1007/s10543-016-0603-3

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