Multivariate polynomial interpolation and meshfree differentiation via undetermined coefficients

摘要

Using undetermined coefficients, we develop a meshfree method to approximate partial derivatives of a multivariate real function from data on a finite set of possibly disordered base points satisfying a natural condition which always holds true in the one dimensional case. The method yields a generalization of Lagrange’s interpolation polynomial and a recursive formula different from Neville’s algorithm.