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.
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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {883--908},
year = {2005},
publisher = {EDP Sciences},
volume = {39},
number = {5},
doi = {10.1051/m2an:2005039},
mrnumber = {2178566},
zbl = {1085.39018},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2005039/}
}
TY - JOUR AU - Sonar, Thomas TI - Difference operators from interpolating moving least squares and their deviation from optimality JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 883 EP - 908 VL - 39 IS - 5 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2005039/ DO - 10.1051/m2an:2005039 LA - en ID - M2AN_2005__39_5_883_0 ER -
%0 Journal Article %A Sonar, Thomas %T Difference operators from interpolating moving least squares and their deviation from optimality %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 883-908 %V 39 %N 5 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2005039/ %R 10.1051/m2an:2005039 %G en %F M2AN_2005__39_5_883_0
Sonar, Thomas. Difference operators from interpolating moving least squares and their deviation from optimality. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 5, pp. 883-908. doi: 10.1051/m2an:2005039
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