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Adaptive Monte Carlo algorithm for Wigner kernel evaluation

  • Venelin TodorovEmail author
  • Ivan Dimov
  • Rayna Georgieva
  • Stoyan Dimitrov
Original Article

Abstract

In this paper, we study numerically various approaches, namely an adaptive Monte Carlo algorithm, a particular rank-1 lattice algorithm based on generalized Fibonacci numbers and a Monte Carlo algorithm based on Latin hypercube sampling for computing multidimensional integrals. We compare the performance of the algorithms over three case studies—multidimensional integrals from Bayesian statistics, the so-called Genz test functions and the Wigner kernel—an important issue in quantum mechanics represented by multidimensional integrals. A comprehensive study and an analysis of the computational complexity of the algorithms under consideration has been presented. Adaptive strategy is well-established as an efficient and reliable tool for multidimensional integration of integrands functions with computational peculiarities like peaks. The presented adaptive Monte Carlo algorithm gives reliable results in computing the Wigner kernel by a stochastic approach that has significantly lower computational complexity than the existing deterministic approaches.

Keywords

Multidimensional integration Adaptive Monte Carlo algorithm Fibonacci lattice sets Latin hypercube sampling Wigner kernel 

Mathematics Subject Classification

65C05 65U05 65F10 65Y20 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Venelin Todorov
    • 1
    • 2
    Email author
  • Ivan Dimov
    • 2
  • Rayna Georgieva
    • 2
  • Stoyan Dimitrov
    • 3
  1. 1.Information Modeling DepartmentInstitute of Mathematics and Informatics, Bulgarian Academy of SciencesSofiaBulgaria
  2. 2.Department of Parallel AlgorithmsInstitute of Information and Communication Technologies, Bulgarian Academy of SciencesSofiaBulgaria
  3. 3.Department of Mathematics, Statistics and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA

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