Accelerating the convergence of the Lanczos algorithm by the use of a complex symmetric Cholesky factorization: application to correlation functions in quantum molecular dynamics

The theoretical description of reactive scattering, photo dissociation and a number of other problems in chemical physics can be formulated in terms of a correlation function between an initial and final state. It is shown by example that the convergence of correlation functions computed using a complex symmetric Lanczos algorithm can be significantly accelerated by using a complex symmetric version of the Cholesky decomposition. In fact, using the standard Lanczos approach without the Cholesky transformation, the correlation function might not converge at all. It is further demonstrated that a stopping criterion for the Lanczos recursions, based on an estimate for the upper bound of the error of the correlation function, can be extended to complex symmetric matrices and used as a reliable stopping criterion for the Cholesky-Lanczos approach.