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
and also give an asymptotic estimate of the quantities
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L. F. Tot, Expansions in the Plane, on the Sphere, and in the Space [in Russian], Fizmatgiz, Moscow (1958).
R. Varga, Functional Analysis and Theory of Approximation in Numerical Analysis [Russian translation], Mir, Moscow (1974).
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Translated from Matematicheskie Zametki, Vol. 18, No. 6, pp. 803–814, December, 1975.
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Babenko, V.F., Ligun, A.A. Interpolation by polyhedral functions. Mathematical Notes of the Academy of Sciences of the USSR 18, 1068–1074 (1975). https://doi.org/10.1007/BF01099983
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DOI: https://doi.org/10.1007/BF01099983