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Difference operators from interpolating moving least squares and their deviation from optimality. (English) Zbl 1085.39018
The interpolating moving least squares method is constructed to prove a theorem on the derivatives of the Shepard interpolant which is the building block of the method i.e. $${d^j\over dx^j} S_f(x_k)= 0$$, $$j= 1,\dots, n-1$$ at every node $$x_k$$. A link between the first and second derivatives based on a linear and quadratic polynomials basis and finite difference operators has also been established.

##### MSC:
 39A70 Difference operators 65D05 Numerical interpolation 65D25 Numerical differentiation 39A12 Discrete version of topics in analysis
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##### References:
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