# 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:

- 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}

}

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