  We present a new Monte Carlo algorithm based on the Stochastic Approximation
Monte Carlo (SAMC) algorithm for directly calculating the density of states.
The proposed method is Stochastic Approximation with a Dynamic update factor
(SAD) which dynamically adjusts the update factor $\gamma_t$ during the course
of the simulation. We test this method on the square-well fluid and the 31-atom
Lennard-Jones cluster and compare the convergence behavior of several related
Monte Carlo methods. We find that both the SAD and $1/t$-Wang-Landau ($1/t$-WL)
methods rapidly converge to the correct density of states without the need for
the user to specify an arbitrary tunable parameter $t_0$ as in the case of
SAMC. SAD requires as input the temperature range of interest, in contrast to
$1/t$-WL, which requires that the user identify the interesting range of
energies. The convergence of the $1/t$-WL method is very sensitive to the
energy range chosen for the low-temperature heat capacity of the Lennard-Jones
cluster. Thus, SAD is more powerful in the common case in which the range of
energies is not known in advance.
