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On a class of spline discrete quasi-interpolants. (English) Zbl 1130.65017

Cohen, Albert (ed.) et al., Curve and surface fitting. Avignon 2006. Proceedings 6th international conference on curves and surfaces, Avignon, France, June 29 – July 5, 2006. Brentwood: Nashboro Press (ISBN 978-0-9728482-8-2/hbk). Modern Methods in Mathematics, 21-30 (2007).
Summary: In general, under mild conditions an expression for the quasi-interpolation error for a sufficiently regular function can be derived involving a term measuring how well the quasi-interpolant approximates the non-reproduced monomials. That term depends on some expressions of the coefficients defining the quasi-interpolant, and it can be minimized.
However, the resulting problem is rather complex and often requires some computational effort. Thus, for discrete quasi-interpolants defined from a piecewise polynomial function \(\varphi\) we propose a simpler minimization problem, based on the Bernstein-Bézier representation of some related piecewise polynomial functions, leading to a new class of discrete quasi-interpolants.
For the entire collection see [Zbl 1112.65002].

MSC:

65D07 Numerical computation using splines
65D05 Numerical interpolation
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