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Neural Computing and Applications
Published in: Neural Computing and Applications 14/2020

02-11-2019 | Original Article

Adaptive Monte Carlo algorithm for Wigner kernel evaluation

Authors: Venelin Todorov, Ivan Dimov, Rayna Georgieva, Stoyan Dimitrov

Published in: Neural Computing and Applications | Issue 14/2020

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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.
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Metadata
Title
Adaptive Monte Carlo algorithm for Wigner kernel evaluation
Authors
Venelin Todorov
Ivan Dimov
Rayna Georgieva
Stoyan Dimitrov
Publication date
02-11-2019
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 14/2020
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-019-04519-9

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