Geodesic
On the permissible class of interpolations for discrete-stochastic procedures of global estimation of functions
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 119-134

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Problems are considered of construction and convergence of numerical discrete-stochastic procedures for approximation of the functions presented in integral form. The procedures include introduction of a discrete grid, estimation of the function at grid nodes using Monte Carlo methods and interpolation of the function using the values at the grid nodes. The results obtained formerly for the multilinear approximation are generalized to the case of interpolation which is based on expanding the function under study in a basis of positive functions forming a partition of unity. The Strang-Fix approximation is considered as an example of such interpolation. The statements are formulated on the rate of convergence of discrete-stochastic procedures for approximation of an integral depending on a parameter. 
@article{SJVM_1998_1_2_a1,
     author = {A. V. Voitishek},
     title = {On the permissible class of interpolations for discrete-stochastic procedures of global estimation of functions},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {119--134},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a1/}
}
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A. V. Voitishek. On the permissible class of interpolations for discrete-stochastic procedures of global estimation of functions. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 119-134. http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a1/