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Title: Solving quadratic lambda-matrix problems without factorization

Abstract

An algorithm is presented for computing the eigenvalues of smallest magnitude and their associated eigenvectors of the quadratic lambda-matrix M lambda/sup 2/ + C lambda + K. M, C, and K are assumed to be symmetric matrices with K positive definite and M negative definite. The algorithm is based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence to the smallest positive and negative eigenvalue is proved. Test examples are presented.

Authors:
;
Publication Date:
Research Org.:
Oak Ridge National Lab., TN (USA)
OSTI Identifier:
6654481
Alternate Identifier(s):
OSTI ID: 6654481
Report Number(s):
ORNL/CSD-76
DOE Contract Number:  
W-7405-ENG-26
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; EIGENVALUES; EIGENVECTORS; MATRICES; MATHEMATICAL LOGIC 990200* -- Mathematics & Computers

Citation Formats

Scott, D.S., and Ward, R.C. Solving quadratic lambda-matrix problems without factorization. United States: N. p., 1981. Web.
Scott, D.S., & Ward, R.C. Solving quadratic lambda-matrix problems without factorization. United States.
Scott, D.S., and Ward, R.C. Sun . "Solving quadratic lambda-matrix problems without factorization". United States.
@article{osti_6654481,
title = {Solving quadratic lambda-matrix problems without factorization},
author = {Scott, D.S. and Ward, R.C.},
abstractNote = {An algorithm is presented for computing the eigenvalues of smallest magnitude and their associated eigenvectors of the quadratic lambda-matrix M lambda/sup 2/ + C lambda + K. M, C, and K are assumed to be symmetric matrices with K positive definite and M negative definite. The algorithm is based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence to the smallest positive and negative eigenvalue is proved. Test examples are presented.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1981},
month = {3}
}

Technical Report:
Other availability
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