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, 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.

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

Nottoli, Tommaso;Gianni', Ivan;Lipparini, Filippo
2023-01-01

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, 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.
2023
Nottoli, Tommaso; Gianni', Ivan; Levitt, A.; Lipparini, Filippo
File in questo prodotto:
File Dimensione Formato  
TCA_LOBPCG.pdf

accesso aperto

Tipologia: Versione finale editoriale
Licenza: Creative commons
Dimensione 1.39 MB
Formato Adobe PDF
1.39 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1203811
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
social impact