Difference operators from interpolating moving least squares and their deviation from optimality
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 5, pp. 883-908.

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

DOI : 10.1051/m2an:2005039
Classification : 39A70, 39A12, 65D05, 65D25
Mots-clés : difference operators, moving least squares interpolation, order of approximation 
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     title = {Difference operators from interpolating moving least squares and their deviation from optimality},
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Sonar, Thomas. Difference operators from interpolating moving least squares and their deviation from optimality. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 5, pp. 883-908. doi : 10.1051/m2an:2005039. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2005039/

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