Several modifications to the Davidson algorithm are systematically
explored to establish their performance for an assortment of configuration
interaction (CI) computations. The combination of a generalized Davidson
method, a periodic two-vector subspace collapse, and a blocked
Davidson approach for multiple roots is determined to retain the
convergence characteristics of the full subspace method. This approach
permits the efficient computation of wave functions for large-scale CI
matrices by eliminating the need to ever store more than three
expansion vectors (**b**_{i}) and associated matrix-vector
products (**sigma**_{i}), thereby dramatically reducing the
I/O requirements relative to the full subspace scheme. The
minimal-storage, single-vector method of Olsen is found to be a reasonable
alternative for obtaining energies of well-behaved systems to within
microhartree accuracy, although it typically requires around 50% more
iterations and at times is too inefficient to yield high accuracy
(ca. 10^{-10} hartree) for very large CI problems. Several
approximations to the diagonal elements of the CI Hamiltonian matrix
are found to allow simple on-the-fly computation of the preconditioning
matrix, to maintain spin symmetry of the determinant-based wave
function, and to preserve the convergence characteristics of the
diagonalization procedure.