The calculation of the numerical information of the general form
l^(N) (F)=(l_N⁽¹⁾(f),...,l_N^(N)(f)
of the volume N about the operator T:F→Y under study, where F is a given functional class, Y is a given
normalized space For each number i e {1,,2,...,N} denotes l^(N) (F) the value of the functional l⁽ⁱ⁾_N, defined on the functional class F
with rare exceptions, cannot be exact. Therefore, the problem arises of finding the limiting error
of the optimal computing unit constructed from numerical information
l^(N) (F) that preserves the exact order of the operator
T:F→Y recovery error and is unimprovable in order in the metric of the normalized space Y.
Concretizing the functional class F, the normalized space Y, the operator
T:F→Y, functionals l⁽ⁱ⁾_N , i=1,2,...,N we obtain various different problems of finding the limiting errors of optimal computing units. In this article, as a class F we use 1 - periodic multidimensional Korobov classes E_S^r, as a space
Y - a space L^{2, ∞} with a mixed norm, as an operator
T:F→Y - a solution of the Cauchy problem for a wave equation with initial conditions f₁ and f₂ from Korobov classes and as functionals  l⁽ⁱ⁾_N , i=1,2,...,N we consider the trigonometric Fourier coefficients of functions f₁ and f₂ and it is proposed for each solution, which is represented as a sum of
absolutely converging multiple functional series, an optimal computing unit with an error (e_N1,e_N2) that preserves the exact discretization order and is unimprovable in order on a power scale in the metric of a normalized space L^{2, ∞}.