  The reweighted random series techniques provide finite-dimensional
approximations to the quantum density matrix of a physical system that have
fast asymptotic convergence. We study two special reweighted techniques that
are based upon the Levy-Ciesielski and Wiener-Fourier series, respectively. In
agreement with the theoretical predictions, we demonstrate by numerical
examples that the asymptotic convergence of the two reweighted methods is cubic
for smooth enough potentials. For each reweighted technique, we propose some
minimalist quadrature techniques for the computation of the path averages.
These quadrature techniques are designed to preserve the asymptotic convergence
of the original methods.
