[For the entire collection see Zbl 0551.00010.]
Optimal recovery means estimating some required feature of a function, known to belong to some specified class of functions, from limited information about it as effectively as possible. The authors propose to consider the areas of optimal recovery not mentioned in, or subsequent to their earlier paper [Optim. Estim. Approx. Theory, Proc. Int. Symp., Freudenstadt 1976, 1-54 (1978; Zbl 0386.93045)]. They present a broad setting for the optimal recovery problem and a sketch of a general theory in normed linear spaces and in Hilbert spaces. The authors also consider the possibility of stochastic and optimal information. In particular they consider optimal interpolation of analytic functions, optimal recovery of best approximations, optimal numerical integration in Sobolev spaces, optimal numerical differentiation and numerical integration of analytic functions. The authors mention the pioneering paper of M. Golomb and H. F. Weinberger [Approx., Proc. Sympos. Math. Res. Center, Madison, April 21-23, 1958, 117-190 (1959; Zbl 0092.058)] and the book of J. F. Traub and H. Woźniakowski [A general theory of optimal algorithms (1980; Zbl 0441.68046)] which has a point of view similar to the authors’ and contains an extensive bibliography.