Multivariate interpolation of arbitrarily spaced data by moving least squares methods

摘要

Given a function f in scattered data points x1,…,xn ∈ RS we solve the least squares problem ∑i=1n∑j=Oqaj(x)bj(xi)-f(xi2vi(X)=minin order to generate interpolants Σaj(x)bj(x). Here the bj denote basis functions, e.g. polynomials, and the vi(x) are inverse distance weight functions. We express the unknowns aj(x), the interpolant and the interpolation error in terms of moving convex combinations of functions corresponding to those of classical interpolation at q + 1 points with respect to these basis functions. Further, we discuss properties of moving least squares methods, and in the case of polynomial basis functions we test various methods and give perspective plots.