Box splines
Bernstein--Bézier representation and near-minimally normed discrete quasi-interpolation operators
Applied Numerical Mathematics
Mathematics and Computers in Simulation
On near-best discrete quasi-interpolation on a four-directional mesh
Journal of Computational and Applied Mathematics
Near-best quasi-interpolants associated with H-splines on a three-direction mesh
Journal of Computational and Applied Mathematics
C2 piecewise cubic quasi-interpolants on a 6-direction mesh
Journal of Approximation Theory
Computer Aided Geometric Design
Advances in Computational Mathematics
Multivariate normalized Powell-Sabin B-splines and quasi-interpolants
Computer Aided Geometric Design
Construction techniques for multivariate modified quasi-interpolants with high approximation order
Computers & Mathematics with Applications
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We consider discrete quasi-interpolants based on C1 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.