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Title: Solving symmetric-definite quadratic lambda-matrix problems without factorization

Abstract

Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda/sup 2/ C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented.

Authors:
 [1];
  1. (Univ. of Texas, Austin)
Publication Date:
OSTI Identifier:
6506875
DOE Contract Number:  
W-7405-ENG-26
Resource Type:
Journal Article
Journal Name:
SIAM J. Sci. Stat. Comput.; (United States)
Additional Journal Information:
Journal Volume: 3:1
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HERMITIAN MATRIX; EIGENVALUES; EIGENVECTORS; ALGORITHMS; CONVERGENCE; EQUATIONS OF MOTION; GYROSCOPES; RITZ METHOD; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL LOGIC; MATRICES; PARTIAL DIFFERENTIAL EQUATIONS; 658000* - Mathematical Physics- (-1987); 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

Citation Formats

Scott, D.S., and Ward, R.C. Solving symmetric-definite quadratic lambda-matrix problems without factorization. United States: N. p., 1982. Web. doi:10.1137/0903005.
Scott, D.S., & Ward, R.C. Solving symmetric-definite quadratic lambda-matrix problems without factorization. United States. doi:10.1137/0903005.
Scott, D.S., and Ward, R.C. Mon . "Solving symmetric-definite quadratic lambda-matrix problems without factorization". United States. doi:10.1137/0903005.
@article{osti_6506875,
title = {Solving symmetric-definite quadratic lambda-matrix problems without factorization},
author = {Scott, D.S. and Ward, R.C.},
abstractNote = {Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda/sup 2/ C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented.},
doi = {10.1137/0903005},
journal = {SIAM J. Sci. Stat. Comput.; (United States)},
number = ,
volume = 3:1,
place = {United States},
year = {1982},
month = {3}
}