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Optimal interpolation of convergent algebraic series

Authors:	S. P. Sidorov

Affiliation:	(1) Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov, 410060, Russian Federation

Abstract:	Let , –1<x ₁<...<x _n<1. Denote $W:=bigl{sum_{r=0}^{infty} a_r t^r: \|a_r\|leq 1, rgeq n bigr}$ , t∈(–1,1). Given a function f∈W we try to recover f(ζ) at fixed point ζ∈(–1,1) by an algorithm A on the basis of the information f(x ₁),...,f(x _n). We find the intrinsic error of recovery $E(W,I):=inf_{A:{mathbb{R}}^nto {mathbb{R}}} sup_{fin W} \|f(zeta)-A(If)\|$ . This work is supported by RFBR (grant 07-01-00167-a and grant 06-01-00003).

Keywords:	Optimal interpolation Lagrange interpolating polynomials
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