Difference operators from interpolating moving least squares and their deviation from optimality
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 5, p. 883-908

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 : https://doi.org/10.1051/m2an:2005039
Classification:  39A70,  39A12,  65D05,  65D25
Keywords: difference operators, moving least squares interpolation, order of approximation
@article{M2AN_2005__39_5_883_0,
     author = {Sonar, Thomas},
     title = {Difference operators from interpolating moving least squares and their deviation from optimality},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {5},
     year = {2005},
     pages = {883-908},
     doi = {10.1051/m2an:2005039},
     zbl = {1085.39018},
     mrnumber = {2178566},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_5_883_0}
}
Sonar, Thomas. Difference operators from interpolating moving least squares and their deviation from optimality. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 5, pp. 883-908. doi : 10.1051/m2an:2005039. http://www.numdam.org/item/M2AN_2005__39_5_883_0/

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