We consider discrete quasi-interpolants based on C^1 quadratic box-splines on uniform criss-cross triangulations of a rectangular domain. The main problem consists in finding good (if not best) coefficient functionals, associated with boundary box-splines, giving both an optimal approximation order and a small infinity norm of the operator. Moreover, we want that these functionals only involve data points inside the domain. They are obtained either by minimizing their infinity norm w.r.t. a finite number of free parameters, or by inducing superconvergence of the operator at some specific points lying near or on the boundary.

Constructing Good Coefficient Functionals for Bivariate $C^1$ Quadratic Spline Quasi-Interpolants

REMOGNA, Sara
2010

Abstract

We consider discrete quasi-interpolants based on C^1 quadratic box-splines on uniform criss-cross triangulations of a rectangular domain. The main problem consists in finding good (if not best) coefficient functionals, associated with boundary box-splines, giving both an optimal approximation order and a small infinity norm of the operator. Moreover, we want that these functionals only involve data points inside the domain. They are obtained either by minimizing their infinity norm w.r.t. a finite number of free parameters, or by inducing superconvergence of the operator at some specific points lying near or on the boundary.
7th International Conference on Mathematical Methods for Curves and Surfaces
Tonsberg, Norvegia
26/06-01/07/2008
Lecture Notes in Computer Science : Mathematical Methods for Curves and Surfaces
Springer
LNCS 5862
329
346
3642116191
9783642116193
Box-splines; Near-best quasi-interpolants; Superconvergence
S. Remogna
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/101398
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