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Bivariate hierarchical Hermite spline quasi-interpolation

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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Acknowledgments

This work was supported by the programs “Finanziamento Giovani Ricercatori 2014” and “Progetti di Ricerca 2015” (Gruppo Nazionale per il Calcolo Scientifico of the Istituto Nazionale di Alta Matematica Francesco Severi, GNCS - INdAM) and by the project DREAMS (MIUR Futuro in Ricerca RBFR13FBI3).

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Correspondence to Alessandra Sestini.

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Communicated by Tom Lyche.

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Bracco, C., Giannelli, C., Mazzia, F. et al. Bivariate hierarchical Hermite spline quasi-interpolation. Bit Numer Math 56, 1165–1188 (2016). https://doi.org/10.1007/s10543-016-0603-3

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  • DOI: https://doi.org/10.1007/s10543-016-0603-3

Keywords

  • B-splines
  • Hermite quasi-interpolation
  • Hierarchical spaces
  • Truncated hierarchical B-splines

Mathematics Subject Classification

  • 65D07
  • 65D15