In a foregoing paper [Sonar, ESAIM: M2AN39 (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 [Dissertation (2001)]. As a typical problem with IMLSmethod we address the question of getting admissible results at the boundary by introducing “ghost points”.Most interesting in IMLS methods are the finite difference operators whichcan be computed from different choices of basis functions and weightfunctions. We present a way of deriving these discrete operators inthe spatially one-dimensional case. Multidimensional operatorscan be constructed by simply extending our approach to higher dimensions.Numerical results ranging from 1-d interpolation to the solution of PDEs are given.

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