  We present a new method for computing the lowest few eigenvalues and the
corresponding eigenvectors of a nuclear many-body Hamiltonian represented in a
truncated configuration interaction subspace, i.e., the no-core shell model
(NCSM). The method uses the hierarchical structure of the NCSM Hamiltonian to
partition the Hamiltonian as the sum of two matrices. The first matrix
corresponds to the Hamiltonian represented in a small configuration space,
whereas the second is viewed as the perturbation to the first matrix.
Eigenvalues and eigenvectors of the first matrix can be computed efficiently.
Perturbative corrections to the eigenvectors of the first matrix can be
obtained from the solutions of a sequence of linear systems of equations
defined in the small configuration space. These correction vectors can be
combined with the approximate eigenvectors of the first matrix to construct a
subspace from which more accurate approximations of the desired eigenpairs can
be obtained. We call this method a Subspace Projection with Perturbative
Corrections (SPPC) method. We show by numerical examples that the SPPC method
can be more efficient than conventional iterative methods for solving
large-scale eigenvalue problems such as the Lanczos, block Lanczos and the
locally optimal block preconditioned conjugate gradient (LOBPCG) method. The
method can also be combined with other methods to avoid convergence stagnation.
