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Title: Solving sparse symmetric generalized eigenvalue problems without factorization

Abstract

In this paper an iterative technique is discussed for finding the algebraic alloy smallest (or largest) eigenvalue of the generalized eigenvalue problem. A-lambda M, where A and M are real, symmetric, and M is positive definite. It is assumed that A and M are such that it is undesirable to factor the matrix A-sigma M for any value of sigma. It is proved that the algorithm is globally convergent, and that convergence is asymptotically quadratic. Finally, the modifications required in the algorithm to make it computationally feasible are discussed.

Authors:
Publication Date:
Research Org.:
Union Carbide Corp., Oak Ridge, TN
OSTI Identifier:
6151892
DOE Contract Number:  
W-7405-ENG-26
Resource Type:
Journal Article
Journal Name:
SIAM J. Numer. Anal.; (United States)
Additional Journal Information:
Journal Volume: 18:1
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; EIGENVALUES; ANALYTICAL SOLUTION; ALGORITHMS; EIGENVECTORS; FACTORIZATION; ITERATIVE METHODS; MATHEMATICS; MATRICES; SYMMETRY; MATHEMATICAL LOGIC; 990200* - Mathematics & Computers

Citation Formats

Scott, D.S. Solving sparse symmetric generalized eigenvalue problems without factorization. United States: N. p., 1981. Web. doi:10.1137/0718008.
Scott, D.S. Solving sparse symmetric generalized eigenvalue problems without factorization. United States. doi:10.1137/0718008.
Scott, D.S. Sun . "Solving sparse symmetric generalized eigenvalue problems without factorization". United States. doi:10.1137/0718008.
@article{osti_6151892,
title = {Solving sparse symmetric generalized eigenvalue problems without factorization},
author = {Scott, D.S.},
abstractNote = {In this paper an iterative technique is discussed for finding the algebraic alloy smallest (or largest) eigenvalue of the generalized eigenvalue problem. A-lambda M, where A and M are real, symmetric, and M is positive definite. It is assumed that A and M are such that it is undesirable to factor the matrix A-sigma M for any value of sigma. It is proved that the algorithm is globally convergent, and that convergence is asymptotically quadratic. Finally, the modifications required in the algorithm to make it computationally feasible are discussed.},
doi = {10.1137/0718008},
journal = {SIAM J. Numer. Anal.; (United States)},
number = ,
volume = 18:1,
place = {United States},
year = {1981},
month = {2}
}