Acceleration of convergence in the polynomial-expanded spectral density approach to bound and resonance state calculations

A procedure is presented for accelerating the convergence of the polynomial-expanded spectral density method for calculating eigenvalues and eigenvectors of a Hamiltonian. After a relatively small number of terms in the expansion, one calculates the scalar spectral function, whose plot gives information on the distribution of the eigenvalues contained in the initial wavepacket. The vectors produced by H acting on the initial vector, combined with the energy-dependent coefficients, are used to construct ‘purified’ and ‘neigborhood basis vectors’, which are used to restart the expansion and to diagonalize the Hamiltonian.