Congratulations to our PhD students Tommaso Nottoli and Ivan Giannì for their publication entitled "A robust, open‐source implementation of the locally optimal block preconditioned conjugate gradient for large eigenvalue problems in quantum chemistry" in the Journal of Theoretical Chemistry Accounts. They 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.
LOBPCG was then tested for various quantum chemistry problems, encompassing medium to large, dense to sparse, well-behaved 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.
