A variation on ref. [2] from 1975 based on a hidden change of
variables in the underlying differential Schroedinger equation
(made popular by Kustaanheimo, P., and Stiefel, E., in 1965 in J.
Reine Angew. Mathematik 218, 204). More explicitly: The well known
linear-algebraist's experience is used that the numerical
inversion of many finite- or infinite-dimensional matrices
J(z)=z-H proves facilitated by their factorization into a product
of an upper triangular and a lower triangular factor. It is known
that for tridiagonal or block-tridiagonal J(z) the factors can be
defined in terms of the scalar- or matrix-valued continued
fractions, respectively. In the text under consideration the
authors specify H as a Hamiltonian and the inverse J(z) as its
Green's function. They demonstrate that for several simple
illustrative numerical examples the reliability as well as the
practical rate of convergence of the search for poles of the
Green's function is simply marvelous.

MR2369975 Kelbert, E.; Hyder, A.; Demir, F.; Hlousek, Z. T.; Papp,
Z. Green's operator for Hamiltonians with Coulomb plus polynomial
potentials. J. Phys. A 40 (2007), no. 27, 7721--7728. 81Q10 (35Q40
47B36)