Geodesic
An error estimation in $\Sigma\Pi$-approximation via statistical methods
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 1, pp. 37-46

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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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     author = {K. I. Kutchinsky},
     title = {An error estimation in $\Sigma\Pi$-approximation via statistical methods},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {37--46},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_1_a3/}
}
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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/