A robust, open-source implementation of the locally optimal block preconditioned conjugate gradient for large eigenvalue problems in quantum chemistry
Abstract
We present two open-source implementations of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) algorithm to find a few eigenvalues and eigenvectors of large, possibly sparse matrices. We then test LOBPCG for various quantum chemistry problems, encompassing medium to large, dense to sparse, wellbehaved to ill-conditioned ones, where the standard method typically used is Davidson's diagonalization. Numerical tests show that, while Davidson's method remains the best choice for most applications in quantum chemistry, LOBPCG represents a competitive alternative, especially when memory is an issue, and can even outperform Davidson for ill-conditioned, non diagonally dominant problems.
Keywords
Cite
@article{arxiv.2305.06668,
title = {A robust, open-source implementation of the locally optimal block preconditioned conjugate gradient for large eigenvalue problems in quantum chemistry},
author = {Tommaso Nottoli and Ivan Giannì and Antoine Levitt and Filippo Lipparini},
journal= {arXiv preprint arXiv:2305.06668},
year = {2023}
}
Comments
Theoretical Chemistry Accounts: Theory, Computation, and Modeling, In press