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On $ (0,1,2)$ interpolation in uniform metric

Authors: J. Szabados and A. K. Varma
Journal: Proc. Amer. Math. Soc. 109 (1990), 975-979
MSC: Primary 41A05; Secondary 41A10
MathSciNet review: 1013983
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Abstract: From the well known theorem of G. Faber it follows that for any given matrix of nodes there exists a continuous function for which the Lagrange interpolation polynomial $ {L_n}[f,x]$, generated by the $ n$ th row of the matrix, does not tend uniformly to $ f(x)$. In this paper we shall provide analogous results for the related operator $ {H_{n,3}}[f,x]$ as defined below.

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