Moving least-squares are Backus-Gilbert optimal
Journal of Approximation Theory
The approximation power of moving least-squares
Mathematics of Computation
Statistical analysis of the moving least-squares method with unbounded sampling
Information Sciences: an International Journal
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The moving-least-squares approach, first presented by McLain [1], is a method for approximating multivariate functions using scattered data information. The method is using local polynomial approximations, incorporating weight functions of different types. Some weights, with certain singularities, induce C^~ interpolation approximation in @?^n. In this work we present a way of generalizing the method to enable Hermite type interpolation, namely, interpolation to derivatives' data as well. The essence of the method is the use of an appropriate metric in the construction of the local polynomial approximations.