English

Bivariate hierarchical Hermite spline quasi--interpolation

Numerical Analysis 2016-02-05 v1

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.

Keywords

Cite

@article{arxiv.1601.02262,
  title  = {Bivariate hierarchical Hermite spline quasi--interpolation},
  author = {Cesare Bracco and Carlotta Giannelli and Francesca Mazzia and Alessandra Sestini},
  journal= {arXiv preprint arXiv:1601.02262},
  year   = {2016}
}
R2 v1 2026-06-22T12:26:23.380Z