Journal
BIT NUMERICAL MATHEMATICS
Volume 56, Issue 4, Pages 1165-1188Publisher
SPRINGER
DOI: 10.1007/s10543-016-0603-3
Keywords
B-splines; Hermite quasi-interpolation; Hierarchical spaces; Truncated hierarchical B-splines
Funding
- program Finanziamento Giovani Ricercatori
- program Progetti di Ricerca
- project DREAMS (MIUR Futuro in Ricerca) [RBFR13FBI3]
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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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