Geodesic
An error estimation in $\Sigma\Pi$-approximation via statistical methods
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 1, pp. 37-46 
K. I. Kutchinsky. An error estimation in $\Sigma\Pi$-approximation via statistical methods. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 1, pp. 37-46. http://geodesic.mathdoc.fr/item/SJVM_1999_2_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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