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Moving Least-Squares: A Numerical Differentiation Method for Irregularly Spaced Calculation Points

Numerical methods may require derivatives of functions whose values are known only on irregularly spaced calculation points. This document presents and quantifies the performance of Moving Least-Squares (MLS), a method of derivative evaluation on irregularly spaced points that has a number of inherent advantages. The user selects both the spatial dimension of the problem and order of the highest conserved moment. The accuracy of calculations is maintained on highly irregularly spaced points. Not required are creation of additional calculation points or interpolation of the calculation points onto a regular grid. Implementation of the method requires the use of only a relatively small number of calculation points. The method is fast, robust and provides smooth results even as the order of the derivative increases.