Direct Minimization for Calculating Invariant Subspaces in Density Functional Computations of the Electronic Structure
Year: 2009
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 2-3 : pp. 360–387
Abstract
In this article, we analyse three related preconditioned steepest descent algorithms, which are partially popular in Hartree-Fock and Kohn-Sham theory as well as invariant subspace computations, from the viewpoint of minimization of the corresponding functionals, constrained by orthogonality conditions. We exploit the geometry of the admissible manifold, i.e., the invariance with respect to unitary transformations, to reformulate the problem on the Grassmann manifold as the admissible set. We then prove asymptotical linear convergence of the algorithms under the condition that the Hessian of the corresponding Lagrangian is elliptic on the tangent space of the Grassmann manifold at the minimizer.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-JCM-8577
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 2-3 : pp. 360–387
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Eigenvalue computation Grassmann manifolds Optimization Orthogonality constraints Hartree-Fock theory Density functional theory PINVIT.