Iterative Shepard operator of least squares thin-plate spline type


We propose a modified bivariate Shepard operator of least squares thin-plate spline type based on an iterative method, introduced by A.V. Masjukov and V.V. Masjukov. This iterative method does not require an artificial setup of the parameters and it is based on successive scaling. For the numerical examples, using an idea of J. R. McMahon, we construct some representative sets of knot points for the initial sets of the interpolation nodes.


Babes-Bolyai University, Faculty of Mathematics and Computer Sciences
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy


Shepard operator; least squares approximation; thin-plate spline; knot points; iterative multiscale method.

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A. Malina, Iterative Shepard operator of least squares thin-plate spline type, Dolomites Res. Notes Approx., 16(2023), No. 3, pp. 57-62.



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Dolomites Research Notes on Approximation

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Padova University Press



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