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BIT Numerical Mathematics
Published in: BIT Numerical Mathematics 3/2014

01-09-2014

Raising the approximation order of multivariate quasi-interpolants

Authors: M. Lamnii, A. Mazroui, A. Tijini

Published in: BIT Numerical Mathematics | Issue 3/2014

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Abstract

Let \({\fancyscript{S}}(\phi _m)\) be the space generated by a finite set \(\phi _m\) of continuous functions defined on a domain \(\varOmega \) in \(\mathbb {R}^s\). We suppose that this space contains the space of polynomials of degree at most \(m\). By using the blossoming approach, we show how to construct multivariate quasi-interpolants which have important properties such as high order of regularity and polynomial reproduction. The quasi-interpolation coefficients are polynomials, obtained as a blossom of a specific polynomial. We will show that some results existing in the literature can be obtained as particular cases to our method.
previous article Accelerated convergence for Schrödinger equations with non-smooth potentials
next article On an exact numerical simulation of solitary-wave solutions of the Burgers–Huxley equation through Cardano’s method

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Metadata
Title
Raising the approximation order of multivariate quasi-interpolants
Authors
M. Lamnii
A. Mazroui
A. Tijini
Publication date
01-09-2014
Publisher
Springer Netherlands
Published in
BIT Numerical Mathematics / Issue 3/2014
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI
https://doi.org/10.1007/s10543-014-0470-8

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