Bernstein--Bézier representation and near-minimally normed discrete quasi-interpolation operators

Authors:
Domingo Barrera-Rosillo;María José Ibáòez-Pérez
Affiliations:
Universidad de Granada, ETS de Ingenieros de Caminos, Canales y Puertos, Departamento de Matemática Aplicada, Campus de Fuentenueva s/n, 18071-Granada, Spain;Universidad de Granada, Facultad de Ciencias, Departamento de Matemática Aplicada, Campus de Fuentenueva s/n, 18071-Granada, Spain
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

We are concerned with the construction of bivariate box-spline discrete quasi-interpolants with small infinity norms and optimal approximation orders. They are defined by minimizing a sharp upper bound of the uniform norm which is derived from the Bernstein-Bezier representation of the corresponding fundamental function. We detail the construction of such quadratic and quartic quasi-interpolants.