We use the Lanczos algorithm for finding eigenvalues and eigenvectors of large sparse real matrices to model atomic nuclei. However, for heavier nuclei and their higher energy states, the matrix elements do not fit into memory. Our idea is therefore to recalculate them on-the-fly in each Lanczos iteration.
However, the matrix element calculation is very time-consuming. Therefore, we would like to reduce the number of iterations needed for reaching the convergence criteria. Would the Block Lanczos possibly help here? Its advantage seems to be when eigenvalues have multiplicities, but this is not our case (eigenvalues correspond with energies of the states, which are distinct). I couldn't find anything about comparing the convergence rate of single-vector and block Lanczos variants.
Or, more generally, is there some other way how to reduce the number of required iterations?