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Zbl 1085.39018
Sonar, Thomas
Difference operators from interpolating moving least squares and their deviation from optimality. (English)
[J] ESAIM, Math. Model. Numer. Anal. 39, No. 5, 883-908 (2005). ISSN 0764-583X; ISSN 1290-3841/e

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.
[B. M. Agrawal (Gwalior)]

MSC 2000:: *39A70 Difference operators
65D05 Interpolation (numerical methods)
65D25 Numerical differentiation
39A12 Discrete version of topics in analysis

Keywords: Difference operators; moving least squares interpolation; order of approximation; Shepard interpolant

Cited in: Zbl 1153.65356

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