  We discuss a method called quasi-sparse eigenvector diagonalization which
finds the most important basis vectors of the low energy eigenstates of a
quantum Hamiltonian. It can operate using any basis, either orthogonal or
non-orthogonal, and any sparse Hamiltonian, either Hermitian, non-Hermitian,
finite-dimensional, or infinite-dimensional. The method is part of a new
computational approach which combines both diagonalization and Monte Carlo
techniques.
