  We report a new multicanonical Monte Carlo (MC) algorithm to obtain the
density of states (DOS) for physical systems with continuous state variables in
statistical mechanics. Our algorithm is able to obtain an analytical form for
the DOS expressed in a chosen basis set, instead of a numerical array of finite
resolution as in previous variants of this class of MC methods such as the
multicanonical (MUCA) sampling and Wang-Landau (WL) sampling. This is enabled
by storing the visited states directly in a data set and avoiding the explicit
collection of a histogram. This practice also has the advantage of avoiding
undesirable artificial errors caused by the discretization and binning of
continuous state variables. Our results show that this scheme is capable of
obtaining converged results with a much reduced number of Monte Carlo steps,
leading to a significant speedup over existing algorithms.
