Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals

Abstract

In this communication, the convergence of the 1/t and Wang - Landau algorithms in the calculation of multidimensional numerical integrals is analyzed. Both simulation methods are applied to a wide variety of integrals without restrictions in one, two and higher dimensions. The errors between the exact and the calculated values of the integral are obtained and the efficiency and accuracy of the methods are determined by their dynamical behavior. The comparison between both methods and the simple sampling Monte Carlo method is also reported. It is observed that the time dependence of the errors calculated with 1/t algorithm goes as N^{-1/2} (with N the MC trials) in quantitative agreement with the simple sampling Monte Carlo method. It is also showed that the error for the Wang - Landau algorithm saturates in time evidencing the non-convergence of the methods. The sources for the error are also determined.

8 pages, 5 figures

References in corpus (4)

• Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error
• Optimal Modification Factor and Convergence of the Wang-Landau Algorithm
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Monte Carlo simulation of joint density of states in one-dimensional Lebwohl-Lasher model using Wang-Landau algorithm

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