A band-Lanczos method for computing matrix elements of a resolvent

The band-Lanczos algorithm is used to compute a few matrix elements of a resolvent, i.e., to compute 〈ψk‖(ω−H)−1‖ψl〉. Here H denotes a Hermitian matrix of large dimension. It is shown that the proposed method which is based on the band-Lanczos algorithm is more efficient than a method based on simple-Lanczos algorithm, e.g., than the residue algebra method. The performance of the Lanczos algorithm (both simple and band) for evaluating resolvents or other functions of H is discussed in some detail.