Open AccessImproved error estimates for an exponentially convergent quadratures
Author(s) -
А. А. Белов,
Н. Н. Калиткин,
Maksim Alexandrovich Tintul
Publication year - 2021
Publication title -
preprint/preprinty ipm im. m.v. keldyša
Language(s) - English
Resource type - Journals
eISSN - 2071-2901
pISSN - 2071-2898
DOI - 10.20948/prepr-2021-8
Subject(s) - sobol sequence , hypercube , mathematics , monte carlo method , unit cube , algorithm , discrete mathematics , statistics
Calculation of the multidimensional cubatures in unit hypercube is a complex problem of numerical methods, and its application value is great. This paper compares various calculation methods: product of regular one-dimensional grid formulae, classical Monte Carlo method using pseudorandom points and the Sobol sequences. It is suggested to use not any Sobol sequences, but only the ones with magic numbers N equal to powers of 2. In addition, the shifted Sobol points are proposed: all coordinates of the magic Sobol points are simultaneously increased by 1/(2N). Comparisons on the test showed that the latter method is significantly more accurate than all the others.