Interpolation by polyhedral functions |
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Authors: | V F Babenko A A Ligun |
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Institution: | 1. Dnepropetrovsk State University and Dneprodzershinsk Industrial Institute, USSR
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Abstract: | A polyhedral functionlp(Δn) (f). interpolating a function f, defined on a polygon Φ, is defined by a set of interpolating nodes Δn ?Φ and a partition P(Δn) of the polygon Φ into triangles with vertices at the points of Δn. In this article we will compute for convex moduli of continuity the quatities $$\begin{gathered} E (H_\Phi ^\omega ; P (\Delta _n )) = sup || f - l_{p(\Delta _n )} (f)||, \hfill \\ f \in H_\Phi ^\omega \hfill \\ \end{gathered} $$ and also give an asymptotic estimate of the quantities $$\begin{gathered} E_n (H_\Phi ^\omega ) = infinf E (H_\Phi ^\omega ; P (\Delta _n )). \hfill \\ \Delta _n P(\Delta _n ) \hfill \\ \end{gathered} $$ |
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