  Estimating the number of eigenvalues located in a given interval of a large
sparse Hermitian matrix is an important problem in certain applications and it
is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often
an exact count is not necessary and methods based on stochastic estimates can
be utilized to yield rough approximations. This paper examines a number of
techniques tailored to this specific task. It reviews standard approaches and
explores new ones based on polynomial and rational approximation filtering
combined with a stochastic procedure.
