Abstract
In the framework of the general statement of the operator reconstruction problem, the problem of discretization of solutions of the heat equation with the initial condition $$f $$ in the periodic anisotropic Sobolev class is solved by computing units constructed from the trigonometric Fourier coefficients $$\hat {f}(m) $$ in the metric of the space $$L^{ \infty ,q} $$ , $$q\geq 2$$ . The error $$\bar {\varepsilon }_{N}$$ of computing the trigonometric Fourier coefficients of the initial condition $$f $$ corresponding to the optimal computing unit is also found, and the sharpness of the order of the error $$\bar {\varepsilon }_{N} $$ is proved.