We present the Preconditioned Locally Harmonic Residual (PLHR) method for
computing a subset of interior eigenvalues and their associated
eigenvectors of a large, possibly sparse, symmetric matrix. The method is
based on a short-term block recurrence, with iteration coefficients given
by the 
-harmonic Rayleigh-Ritz procedure. PLHR does not require
traditional spectral transformations, matrix factorizations, or
inversions. Instead, it takes advantage of symmetric positive definite
preconditioning. We describe a simple derivation of the algorithm, which
is motivated by a relation between interior eigensolvers and
preconditioned linear solvers for symmetric indefinite systems, and
discuss possible preconditioning approaches. Several numerical
experiments will be presented to illustrate efficiency and robustness of
the algorithm.