Analysis of the convergence of the 1t and Wang-Landau algorithms in the calculation of multidimensional integrals.
In this Brief Report, the convergence of the 1t 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 efficiency and accuracy of both algorithms are determined by the dynamical behavior of the errors between the exact and the calculated values of the integral. It is observed that the time dependence of the error calculated with the 1t algorithm varies as N;{-12} [with N the number of Monte Carlo (MC) trials], in quantitative agreement with the simple sampling Monte Carlo method. In contrast, the error calculated with the Wang-Landau algorithm saturates in time, evidencing the nonconvergence of this method. The sources of error for both methods are also determined.
Belardinelli
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Departamento de Física, Instistuto Nacional de Física Aplicada, Universidad Nacional de San Luis, CONICET, Chacabuco 917,5700 San Luis, Argentina. rbelar@unsl.edu.ar
Manzi
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Pereyra
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