Robust and efficient density fitting

Abstract

In this paper we propose an iterative method for solving the inhomogeneous systems of linear equations associated with density fitting. The proposed method is based on a version of the conjugate gradient method that makes use of automatically built quasi-Newton preconditioners. The paper gives a detailed description of a parallel implementation of the new method. The computational performance of the new algorithms is analyzed by benchmark calculations on systems with up to about 35,000 auxiliary functions. Comparisons with the standard, direct approach show no significant differences in the computed solutions.