  A new method for computing the density of states in nuclei making use of an
extrapolated form of the tri-diagonal matrix obtained from the Lanczos method
is presented. It will be shown that the global, average properties of the
entire Lanczos matrix can be predicted from just four Lanczos iterations. The
extrapolated Lanczos matrix (ELM) approach provides for an accurate computation
of the density of states described within the configuration space, which, in
some cases, is sufficient to accurately calculate the density of states at, or
near, the neutron separation energy. Comparisons between theory and experiment
are shown for $^{57}$Fe, $^{74}$Ge, and $^{76}$Ge. In addition, we show results
for the $J$-dependence of moments and the level density for these three nuclei.
