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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. Ismagilov

1

ismagil@bmstu.ru

L.E. Filippova

2

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).