Abstract:
The optimal recovery of values of linear operators is considered for classes of elements the information on which is known with a stochastic error. Linear optimal recovery methods are constructed that, in general, do not use all the available information for the measurements. As a consequence, an optimal method is described for recovering a function from a finite set of its Fourier coefficients specified with a stochastic error.
Bibliography: 14 titles.
Keywords:optimal recovery, minimax estimation, Fourier coefficients, extremal problem, linear operator.