Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 463.41002
Autor: Erdös, Paul; Vertesi, P.
Title: On the almost everywhere divergence of Lagrange interpolatory polynomials for arbitrary system of nodes. (In English)
Source: Acta Math. Acad. Sci. Hung. 36, 71-89 (1980); correction ibid. 38, 263 (1981); corrections also in Geombinatorics 2, No.2, 37 (1992).
Review: In this paper we give a detailed proof of the conjecture of P.Erdös [ibid. 9, 381-388(1938; Zbl 083.29001)]: If X = {xkn}. 1 \leq k \leq n, n = 1,2,..., is an interpolatory matrix in [-1,1] then there exists a continous function on [-1,1], F(x), for which lim\supn ––> oo|Ln(F,X,x)| = oo almost everywhere in [-1,1]. here Ln(F,X,x) is the Lagrange interpolatory polynomial of F(x) based on x1n,x2n,...,xnn.
Classif.: * 41A05 Interpolation
Keywords: Lagrange interpolatory polynomial
Citations: Zbl.083.29001
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag