  We introduce an iterative importance truncation scheme which aims at reducing
the dimension of the model space of configuration interaction approaches by an
a priori selection of the physically most relevant basis states. Using an
importance measure derived from multiconfigurational perturbation theory in
combination with an importance threshold, we construct a model space optimized
for the description of individual eigenstates of a given Hamiltonian. We
discuss in detail various technical aspects and refinements of the importance
truncation, such as perturbative corrections for excluded basis states,
threshold extrapolation techniques, and different iterative model-space update
schemes. We apply the idea of the importance truncation in the context of the
no-core shell model (NCSM) for the ab initio description of nuclear ground
states. In a series of benchmark calculations for closed- and open-shell nuclei
up to O-16 we compare the ground-state energies obtained in the importance
truncated NCSM to the full NCSM. All calculations show an excellent agreement
of importance truncated and full NCSM for all cases where the latter is
feasible. The results demonstrate that the importance truncated NCSM, while
preserving most of the advantages of the full NCSM, gives access to much larger
N_max*hbar*Omega spaces and heavier nuclei. In this way we are able to perform
importance truncated NCSM calculations for nuclei like C-12 and O-16 up to
N_max=22.
