DIRECT MINIMIZATION FOR CALCULATING INVARIANT SUBSPACES IN DENSITY FUNCTIONAL COMPUTATIONS OF THE ELECTRONIC STRUCTURE

• 来源期刊: 计算数学（英文版）
• 关键词: Eigenvalue computation Grassmann manifolds Optimization Orthogonality constraints Hartree-Fock theory Density functional theory PINVIT
• 年，卷（期）: 2009,（2）
• 页码范围: 360-387
• 页数: 28页
• 语种: 英文

摘要

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 Crassmann manifold at the minimizer.