@Article{JCM-27-360,
author = {Reinhold Schneider, Thorsten Rohwedder, Alexey Neelov and Johannes Blauert},
title = {Direct Minimization for Calculating Invariant Subspaces in Density Functional Computations of the Electronic Structure},
journal = {Journal of Computational Mathematics},
year = {2009},
volume = {27},
number = {2-3},
pages = {360--387},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/8577.html}
}