Computing charge densities with partially reorthogonalized Lanczos

This paper considers the problem of computing charge densities in a density functional theory (DFT) framework. In contrast to traditional, diagonalization-based, methods, we utilize a technique which exploits a Lanczos basis, without explicit reference to individual eigenvectors. The key ingredient of this new approach is a partial reorthogonalization strategy whose goal is to ensure a good level of orthogonality of the basis vectors. The experiments reveal that the method can be a few times faster than ARPACK, the implicit restart Lanczos method. This is achievable by exploiting more memory and BLAS3 (dense) computations while avoiding the frequent updates of eigenvectors inherent to all restarted Lanczos methods.