Multivariate polynomial interpolation and meshfree differentiation via undetermined coefficients

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.

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