Preconditioned gradient flows for nonlinear eigenvalue problems and application to the Hartree-Fock functional

✍ Scribed by François Alouges; Christophe Audouze

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 491 KB
• Volume: 25
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.20347

✦ Synopsis

Abstract

In this article, we propose to solve numerically the problem of finding the smallest eigenvalues of a Hermitian operator (and the space spanned by the corresponding eigenvectors) by a gradient flow technique. This method is then applied to the Hartree‐Fock problem. Improvements are also proposed in two directions: preconditioning of the dynamical system and development of a specific flow that enables to compute directly the eigenvectors. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009