An error estimation in $\Sigma\Pi$-approximation via statistical methods

This paper offers a statistical approach to obtain a numerical estimate of $\Sigma\Pi$-approximation algorithm efficiency on a fixed functional class. This approach consists of two steps. The first one is finding the distribution of $\Sigma\Pi$-approximation coefficients. The second one is the simulation of a random vector with obtained probability density and calculation the integer $s$ (number of summands in $\Sigma\Pi$-series) that provides given accuracy with given probability.