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}
}
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