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Article Dans Une Revue Theoretical Chemistry Accounts: Theory, Computation, and Modeling Année : 2023

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

Résumé

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.
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Dates et versions

hal-04094087 , version 1 (10-05-2023)

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Tommaso Nottoli, Ivan Giannı̀, Antoine Levitt, Filippo Lipparini. A robust, open-source implementation of the locally optimal block preconditioned conjugate gradient for large eigenvalue problems in quantum chemistry. Theoretical Chemistry Accounts: Theory, Computation, and Modeling, inPress. ⟨hal-04094087⟩
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