Abstract
This paper investigates the optimal recovery of a class F∞ of infinitely differentiable functions on [−1,1] in Lp[−1,1]. We obtain strong equivalences of the sampling numbers of F∞ in Lp[−1,1],1≤p<∞, and even equality in L∞[−1,1]. We prove that the Lagrange interpolation algorithms In,p,1≤p≤∞, based on the zeros of the polynomial of degree n with the leading coefficient 1 of the least deviation from zero in Lp[−1,1] are strongly asymptotically optimal for 1≤p<∞, and optimal for p=∞.
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