Difference operators from interpolating moving least squares and their deviation from optimality
Institut Computational Mathematics, TU Braunschweig,
38106 Braunschweig, Germany. firstname.lastname@example.org
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.
Mathematics Subject Classification: 39A70 / 39A12 / 65D05 / 65D25
Key words: Difference operators / moving least squares interpolation / order of approximation.
© EDP Sciences, SMAI, 2005