DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Spectral Schur complement techniques for symmetric eigenvalue problems

Abstract

This paper presents a domain decomposition-type method for solving real symmetric (Hermitian) eigenvalue problems in which we seek all eigenpairs in an interval [α; β] or a few eigenpairs next to a given real shift. Here, a Newton-based scheme is described whereby the problem is converted to one that deals with the interface nodes of the computational domain. This approach relies on the fact that the inner solves related to each local subdomain are relatively inexpensive. This Newton scheme exploits spectral Schur complements, and these lead to so-called eigenbranches, which are rational functions whose roots are eigenvalues of the original matrix. Theoretical and practical aspects of domain decomposition techniques for computing eigenvalues and eigenvectors are discussed. A parallel implementation is presented and its performance on distributed computing environments is illustrated by means of a few numerical examples.

Authors:
 [1];  [1];  [1]
  1. Univ. of Minnesota, Minneapolis, MN (United States). Computer Science & Engineering
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
OSTI Identifier:
1438784
Report Number(s):
LLNL-JRNL-691697
Journal ID: ISSN 1068-9613
Grant/Contract Number:  
AC52-07NA27344; SC0008877; NSF/DMS-1216366
Resource Type:
Accepted Manuscript
Journal Name:
Electronic Transactions on Numerical Analysis
Additional Journal Information:
Journal Volume: 45; Journal ID: ISSN 1068-9613
Publisher:
Kent State University - Johann Radon Institute for Computational and Applied Mathematics (RICAM)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Domain decomposition; spectral Schur complements; eigenvalue problems; Newton’s method; parallel computing

Citation Formats

Li, Ruipeng, Kalantzis, Vassilis, and Saad, Yousef. Spectral Schur complement techniques for symmetric eigenvalue problems. United States: N. p., 2016. Web.
Li, Ruipeng, Kalantzis, Vassilis, & Saad, Yousef. Spectral Schur complement techniques for symmetric eigenvalue problems. United States.
Li, Ruipeng, Kalantzis, Vassilis, and Saad, Yousef. Fri . "Spectral Schur complement techniques for symmetric eigenvalue problems". United States. https://www.osti.gov/servlets/purl/1438784.
@article{osti_1438784,
title = {Spectral Schur complement techniques for symmetric eigenvalue problems},
author = {Li, Ruipeng and Kalantzis, Vassilis and Saad, Yousef},
abstractNote = {This paper presents a domain decomposition-type method for solving real symmetric (Hermitian) eigenvalue problems in which we seek all eigenpairs in an interval [α; β] or a few eigenpairs next to a given real shift. Here, a Newton-based scheme is described whereby the problem is converted to one that deals with the interface nodes of the computational domain. This approach relies on the fact that the inner solves related to each local subdomain are relatively inexpensive. This Newton scheme exploits spectral Schur complements, and these lead to so-called eigenbranches, which are rational functions whose roots are eigenvalues of the original matrix. Theoretical and practical aspects of domain decomposition techniques for computing eigenvalues and eigenvectors are discussed. A parallel implementation is presented and its performance on distributed computing environments is illustrated by means of a few numerical examples.},
doi = {},
journal = {Electronic Transactions on Numerical Analysis},
number = ,
volume = 45,
place = {United States},
year = {Fri Sep 02 00:00:00 EDT 2016},
month = {Fri Sep 02 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
The DOI is not currently available

Save / Share: