Optimal recovery of the derivative of bounded analytic functions

Given ζ ∈ (-1, 0), n ∈ N, we discuss the optimal recovery of f{hook} (ζ), for f{hook} analytic and bounded in . |Z|&<1 < 1, from the knowledge of the values of f{hook} at n points z1,.zm∈[0,l), where these points are chosen to produce the least possible intrinsic error. The optimal algorithms are explicitly determined. © 1983 Academic Press Inc. (London) Limited.