A B-spline Tensor for Vectorial Quasi-Interpolant
INSTITUT NATIONAL DES SCIENCES APPLIQUEES DE TOULOUSE (FRANCE) GENIE MATHEMATIQUE ET MODELISATION
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The aim of this paper is to introduce new techniques and new tools for vector field approximation. We do so by building the equivalent of B-splines, which are now tensor B-splines, as shown below, and by appling to the discretization based on a regular grid of a differential operator a fundamental solution of it, as done for polynomial B-splines and polyharmonic B-splines. We thus obtain quasi-interpolants in the vectorial case whose properties generalize the properties of the quasi-interpolants generated by using B-splines. All this is done in the case when the data lie on a regular infinite grid.
- Numerical Mathematics
- Theoretical Mathematics