The order of the best transfinite interpolation of functions with bounded laplacian with the help of harmonic splines on box partitions

D. Skorokhodov

doi:10.15421/241811

The order of the best transfinite interpolation of functions with bounded laplacian with the help of harmonic splines on box partitions

D. Skorokhodov (Oles Honchar Dnipro National University), https://orcid.org/0000-0001-8494-5885

Abstract

We show that the error of the best transfinite interpolation of functions with bounded laplacian with the help of harmonic splines on box partitions comprising $$$N$$$ elements has the order $$$N^{-2}$$$ as $$$N \rightarrow \infty$$$.

Keywords

transfinite interpolation; best approximation; harmonic spline

MSC 2020

41A05; 41A15; 41A50; 46E30

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