Geodesic
On some special effects in theory on numerical integration and functions recovery
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2018), pp. 96-102

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We discuss two questions. First, we consider the existence of close to optimal quadrature formulas with a bad $L^2$-discrepancy of their grids, and the second is the question of how much explicit quadrature formulas are preferable to sorting algorithms. Also, in the model case, we obtaine the solution to the question of approximative possibilities of Smolyak's grid in the problems of recovery of functions.
Keywords: discrepancy in uniform and integral metrics, Smolyak's grid, Korobov's grid, approximative possibilities of a specific computational aggregate, sorting algorithms in problems of numerical integration.
Mots-clés : explicit quadrature formula 
@article{IVM_2018_3_a10,
     author = {N. Zh. Nauryzbaev and A. A. Shomanova and N. Temirgaliyev},
     title = {On some special effects in theory on numerical integration and functions recovery},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {96--102},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_3_a10/}
}
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N. Zh. Nauryzbaev; A. A. Shomanova; N. Temirgaliyev. On some special effects in theory on numerical integration and functions recovery. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2018), pp. 96-102. http://geodesic.mathdoc.fr/item/IVM_2018_3_a10/