The average dimension of a multidimensional function for quasi-Monte Carlo estimates of an integral
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 12, pp. 2159-2165
The effective dimension of a multidimensional function was previously introduced to measure the complexity of the function with respect to the evaluation of an integral by quasi-Monte Carlo methods. For the same goal, the concept of the average dimension is introduced, which, in contrast to the effective dimension, is independent of an arbitrary confidence level.
@article{ZVMMF_2006_46_12_a4,
author = {D. I. Asotskii and E. E. Myshetskaya and I. M. Sobol'},
title = {The average dimension of a~multidimensional function for {quasi-Monte} {Carlo} estimates of an integral},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {2159--2165},
year = {2006},
volume = {46},
number = {12},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a4/}
}
TY - JOUR AU - D. I. Asotskii AU - E. E. Myshetskaya AU - I. M. Sobol' TI - The average dimension of a multidimensional function for quasi-Monte Carlo estimates of an integral JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2006 SP - 2159 EP - 2165 VL - 46 IS - 12 UR - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a4/ LA - ru ID - ZVMMF_2006_46_12_a4 ER -
%0 Journal Article %A D. I. Asotskii %A E. E. Myshetskaya %A I. M. Sobol' %T The average dimension of a multidimensional function for quasi-Monte Carlo estimates of an integral %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2006 %P 2159-2165 %V 46 %N 12 %U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a4/ %G ru %F ZVMMF_2006_46_12_a4
D. I. Asotskii; E. E. Myshetskaya; I. M. Sobol'. The average dimension of a multidimensional function for quasi-Monte Carlo estimates of an integral. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 12, pp. 2159-2165. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a4/