Abstract
For the Klein-Gordon equation with initial conditions in Nikol’skii classes, we obtain sharp orders of discretization errors with respect to precise information. In particular, these orders imply qualitatively and quantitatively that raising the smoothness of one of the initial conditions relative to the other does not improve the discretization characteristics of the solution of the equation. Bounds for information distortion are given under which the limit possible errors, i.e., discretization errors with respect to precise information, are still maintained. This is important because superfluous computational accuracy used when implementing an algorithm results in an unjustified increase in memory requirements and the number of arithmetic operations without improving the accuracy inherent to the algorithm. The quality of approximation aggregates is also estimated in mean square with respect to probability measures on Nikol’skii classes.