It is shown that various numerical methods to compute densities of states, projected densities of states (relevant for light scattering spectra), electrical or elastic properties of disordered media can all be considered as special cases of a general approach to these problems. This approach is based on a recursive evaluation of a generating function which in appropriate limits reduces, for example, to the approach based on the negative-eigenvalue theorem or to Gaussian elimination optimized for symmetric sparse matrices. The approach is simple and systematic. It also leads to an alternate proof of the negative-eigenvalue theorem. The general formalism and various special cases are discussed in detail. Comparisons with other methods such as the transfer-matrix, conjugate-gradient, and Haydock-Lanczos methods are provided.

• Received 15 December 1986

DOI:https://doi.org/10.1103/PhysRevB.36.1463