In this paper the problems of recovering functions and finding the limiting error of the optimal computing unit are solved in the case when the numerical information of the volume N about the restored function f, belonging to the generalized multidimensional Sobolev classes, is removed from the linear functionals defined on the classes under consideration.The relevance of this work is due to the following factors: firstly, the problem of restoring functions from a functional class F by computing units constructed from the values of linear functionals is attractive because the computing units form a fairly wide set containing all partial sums of Fourier series over all possible orthonormal systems as well as all finite approximation sums used in orthowidths, linear widths and greedy algorithms; secondly, the calculation of numerical information about a function f, with rare exceptions, cannot be accurate. Therefore, finding the limiting error of the optimal computing unit, that preserves the exact order of the recovery error and is unimprovable in order is an important problem in approximation theory and numerical analysis; thirdly, previously, the problem of finding the limiting error of an optimal computing unit was not studied on functional classes of Sobolev with generalized smoothness.