Polar forms and quadratic spline quasi-interpolants on Powell--Sabin partitions

Authors:
D. Sbibih;A. Serghini;A. Tijini
Affiliations:
University Mohammed I, ESTO, MATSI Laboratory, Oujda, Morocco;University Mohammed I, ESTO, MATSI Laboratory, Oujda, Morocco;University Mohammed I, ESTO, MATSI Laboratory, Oujda, Morocco
Venue:
Applied Numerical Mathematics
Year:
2009

Citing 5
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Abstract

In this paper we introduce the Powell-Sabin B-spline representation of quadratic polynomials or splines in terms of their polar forms. We use this B-representation for constructing several differential or discrete quasi-interpolants which have an optimal approximation order. This new approach is simple and provides an efficient tool for describing many schemes of approximation involving values and (or) derivatives of a given function.