Geodesic
Error estimation for multidimensional analogue of the polygon of frequencies method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 1, pp. 11-24

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Decomposition to three components for $L_2$-error of multi-dimensional analogue of the polygon of frequencies method is obtained. For every component an upper bound is constructed. The statement about the finiteness of maximum of variances of stochastic estimates in grid nodes is derived. Upper bounds for displacements of estimates in nodes for $C$-approach and $L_2$-approach are obtained. On that basis it is shown that the application of smooth approximations of the solution for the polygon of frequencies method is inexpedient. 
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     author = {A. V. Voitishek and N. G. Golovko and E. V. Shkarupa},
     title = {Error estimation for multidimensional analogue of the polygon of frequencies method},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2002_5_1_a1/}
}
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A. V. Voitishek; N. G. Golovko; E. V. Shkarupa. Error estimation for multidimensional analogue of the polygon of frequencies method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 1, pp. 11-24. http://geodesic.mathdoc.fr/item/SJVM_2002_5_1_a1/