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.
We consider the classical Interpolating Moving Least Squares (IMLS)
interpolant as defined by Lancaster and Šalkauskas [
(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.
In a foregoing paper [Sonar,
(2005) 883–908] we analyzed the Interpolating Moving Least Squares (IMLS) method due to Lancaster and Šalkauskas with respect to its approximation powers and derived finite difference expressions for the derivatives. In this sequel we follow a completely different approach to the IMLS method given by Kunle [ (2001)]. As a typical problem with IMLS
method we address the question of getting admissible results at the boundary
by introducing “ghost points”.
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