English

A robust, open-source implementation of the locally optimal block preconditioned conjugate gradient for large eigenvalue problems in quantum chemistry

Numerical Analysis 2023-05-12 v1 Numerical Analysis

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

R2 v1 2026-06-28T10:31:50.472Z