Вероятностные оценки погрешности формул приближенного интегрирования для функций многих переменных

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Р.С. Исмагилов, Л.E. Филиппова
20 ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2017. № 2
PROBABILISTIC ERROR ESTIMATION IN APPROXIMATE INTEGRATION
FORMULAS FOR MULTIVARIABLE FUNCTIONS
R.S. Ismagilov1
L.E. Filippova2
1 Bauman Moscow State Technical University, Moscow, Russian Federation
2 Higher School of Economics Tikhonov Moscow Institute of Electronics and Mathematics,
Moscow, Russian Federation
Abstract Keywords
The study examines the problem of approximate integra-
tion of multivariable functions. These functions are taken
from the space with Gaussian measure. According to it, we
calculated the average value of the integral standard devia-
tion from the integral sum. The paper gives the vanishing
order for the standard deviation depending on the parame-
ters that define the integral sum. We obtained probabilistic
estimates of approximate integration errors
Approximate integration, Gaussian
measure, multivariable function,
probabilistic estimates
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Ismagilov R.S. — Dr. Sc. (Phys.-Math.), Professor of Higher Mathematics Department,
Bauman Moscow State Technical University (2-ya Baumanskaya ul. 5, Moscow, 105005 Rus-
sian Federation).
Filippova L.E. — Assoc. Professor, School of Applied Mathematics, Higher School of Eco-
nomics Tikhonov Moscow Institute of Electronics and Mathematics (Myasnitskaya ul. 20,
Moscow, 101000 Russian Federation).