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Difference operators from interpolating moving least squares and theirdeviation from optimality

Published online by Cambridge University Press:  15 September 2005

Thomas Sonar
Thomas Sonar*
Affiliation:
Institut Computational Mathematics, TU Braunschweig, Pockelsstraße 14, 38106 Braunschweig, Germany. [email protected]
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Abstract

We consider the classical Interpolating Moving Least Squares (IMLS)interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981) 141–158] andcompute the first and second derivative of this interpolant at the nodes of agiven grid with the help of a basic lemma on Shepard interpolants. We comparethe difference formulae with those defining optimal finite difference methods anddiscuss their deviation from optimality.

Keywords

Difference operatorsmoving least squares interpolationorder of approximation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 5 , September 2005 , pp. 883 - 908
Copyright
© EDP Sciences, SMAI, 2005

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