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Title: Asymptotic convergence for iterative optimization in electronic structure

Abstract

There have recently been a number of proposals for solving large electronic structure problems (local-density approximation, Hartree-Fock, and tight-binding methods) iteratively with a computational effort proportional to the size of the system. The effort needed to perform a single iteration in these schemes is well understood but the convergence rate has been an empirical matter. This paper will show that many of the proposed methods have a single underlying geometrical structure, which has a specific asymptotic convergence behavior, and that behavior can be understood in terms of some simple condition numbers based on the spectrum of the Hamiltonian. (c) 2000 The American Physical Society.

Authors:
 [1];  [1]
  1. Sandia National Laboratories, MS 1110, Albuquerque, New Mexico 87185 (United States)
Publication Date:
OSTI Identifier:
20216424
Resource Type:
Journal Article
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 61; Journal Issue: 19; Other Information: PBD: 15 May 2000; Journal ID: ISSN 1098-0121
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ELECTRONIC STRUCTURE; ITERATIVE METHODS; ASYMPTOTIC SOLUTIONS; CONVERGENCE; HAMILTONIANS; ALGORITHMS; OPTIMIZATION; THEORETICAL DATA

Citation Formats

Lippert, Ross A., and Sears, Mark P. Asymptotic convergence for iterative optimization in electronic structure. United States: N. p., 2000. Web. doi:10.1103/PhysRevB.61.12772.
Lippert, Ross A., & Sears, Mark P. Asymptotic convergence for iterative optimization in electronic structure. United States. doi:10.1103/PhysRevB.61.12772.
Lippert, Ross A., and Sears, Mark P. Mon . "Asymptotic convergence for iterative optimization in electronic structure". United States. doi:10.1103/PhysRevB.61.12772.
@article{osti_20216424,
title = {Asymptotic convergence for iterative optimization in electronic structure},
author = {Lippert, Ross A. and Sears, Mark P.},
abstractNote = {There have recently been a number of proposals for solving large electronic structure problems (local-density approximation, Hartree-Fock, and tight-binding methods) iteratively with a computational effort proportional to the size of the system. The effort needed to perform a single iteration in these schemes is well understood but the convergence rate has been an empirical matter. This paper will show that many of the proposed methods have a single underlying geometrical structure, which has a specific asymptotic convergence behavior, and that behavior can be understood in terms of some simple condition numbers based on the spectrum of the Hamiltonian. (c) 2000 The American Physical Society.},
doi = {10.1103/PhysRevB.61.12772},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {1098-0121},
number = 19,
volume = 61,
place = {United States},
year = {2000},
month = {5}
}