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KIAM Preprint № 8, Moscow, 2021
Authors: Belov A.A., Kalitkin N.N., Tintul M.A.
Improved error estimates for an exponentially convergent quadratures
Abstract:
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.
Keywords:
multidimensional cubatures, Monte Carlo method, Sobol sequences, magic numbers, shifted Sobol points
Publication language: russian,  pages: 24
Research direction:
Mathematical modelling in actual problems of science and technics
Russian source text:
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About authors:
  • Belov Alexander Alexandrovich,  orcid.org/0000-0002-0918-9263,  M.V. Lomonosov MSU, Faculty of Physics; PFUR
  • Kalitkin Nikolaj Nikolaevich,  orcid.org/0000-0002-0861-1792KIAM RAS
  • Tintul Maksim Alexandrovich,  orcid.org/0000-0002-5466-1221,  M.V. Lomonosov MSU, Faculty of Physics