Geodesic
Average discrepancy for periodic integrands
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 4, pp. 353-362

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In the numerical integration of periodic integrands over the $s$-dimensional unit cube, various performance criteria such as $P_{\alpha}$ and $R$ have previously been used. In this paper, we use a criterion called $L_2$ discrepancy. An analogue of this quantity has previously been used to study the error in the case of non-periodic integrands. For this quantity we obtain expressions for the average in the case of number-theoretic and $2^s$ copy rules. The values of these averages are then compared for roughly the same number of points 
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     author = {M. V. Reddy},
     title = {Average discrepancy for periodic integrands},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {353--362},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a7/}
}
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M. V. Reddy. Average discrepancy for periodic integrands. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 4, pp. 353-362. http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a7/