skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Solving a Class of Nonlinear Eigenvalue Problems by Newton's Method

Abstract

We examine the possibility of using the standard Newton's method for solving a class of nonlinear eigenvalue problems arising from electronic structure calculation. We show that the Jacobian matrix associated with this nonlinear system has a special structure that can be exploited to reduce the computational complexity of the Newton's method. Preliminary numerical experiments indicate that the Newton's method can be more efficient for small problems in which a few smallest eigenpairs are needed.

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
Computational Research Division
OSTI Identifier:
965775
Report Number(s):
LBNL-2187E
TRN: US200922%%511
DOE Contract Number:  
DE-AC02-05CH11231
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97; EIGENVALUES; ELECTRONIC STRUCTURE; NONLINEAR PROBLEMS; nonlinear eigenvalue problem, Newton's method

Citation Formats

Gao, Weiguo, Yang, Chao, and Meza, Juan C. Solving a Class of Nonlinear Eigenvalue Problems by Newton's Method. United States: N. p., 2009. Web. doi:10.2172/965775.
Gao, Weiguo, Yang, Chao, & Meza, Juan C. Solving a Class of Nonlinear Eigenvalue Problems by Newton's Method. United States. https://doi.org/10.2172/965775
Gao, Weiguo, Yang, Chao, and Meza, Juan C. 2009. "Solving a Class of Nonlinear Eigenvalue Problems by Newton's Method". United States. https://doi.org/10.2172/965775. https://www.osti.gov/servlets/purl/965775.
@article{osti_965775,
title = {Solving a Class of Nonlinear Eigenvalue Problems by Newton's Method},
author = {Gao, Weiguo and Yang, Chao and Meza, Juan C},
abstractNote = {We examine the possibility of using the standard Newton's method for solving a class of nonlinear eigenvalue problems arising from electronic structure calculation. We show that the Jacobian matrix associated with this nonlinear system has a special structure that can be exploited to reduce the computational complexity of the Newton's method. Preliminary numerical experiments indicate that the Newton's method can be more efficient for small problems in which a few smallest eigenpairs are needed.},
doi = {10.2172/965775},
url = {https://www.osti.gov/biblio/965775}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Jul 02 00:00:00 EDT 2009},
month = {Thu Jul 02 00:00:00 EDT 2009}
}