Locally Determined Smooth Interpolation at Irregularly Spaced Points in Several Variables

Abstract

A class of methods for local interpolation at irregularly spaced points for functions of two or more variables is developed. The methods are based on a weighted average of the values of local interpolating functions, with the local interpolating functions and the weighting functions chosen so as to incorporate the desired smoothness. Numerical results for several interpolation functions from this class are compared with global approximations, some of which are local when implemented on a computer.