  We examine and compare several iterative methods for solving large-scale
eigenvalue problems arising from nuclear structure calculations. In particular,
we discuss the possibility of using block Lanczos method, a Chebyshev filtering
based subspace iterations and the residual minimization method accelerated by
direct inversion of iterative subspace (RMM-DIIS) and describe how these
algorithms compare with the standard Lanczos algorithm and the locally optimal
block preconditioned conjugate gradient (LOBPCG) algorithm. Although the
RMM-DIIS method does not exhibit rapid convergence when the initial
approximations to the desired eigenvectors are not sufficiently accurate, it
can be effectively combined with either the block Lanczos or the LOBPCG method
to yield a hybrid eigensolver that has several desirable properties. We will
describe a few practical issues that need to be addressed to make the hybrid
solver efficient and robust.
