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Solving Symmetric-Definite Quadratic $$\lambda $$-Matrix Problems without Factorization

Journal Article · · SIAM Journal on Scientific and Statistical Computing
DOI:https://doi.org/10.1137/0903005· OSTI ID:6654481
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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.

Research Organization:
Oak Ridge National Lab., TN (USA)
Sponsoring Organization:
USDOE
Grant/Contract Number:
W-7405-ENG-26
OSTI ID:
6654481
Alternate ID(s):
OSTI ID: 6506875
Report Number(s):
ORNL/CSD-76
Journal Information:
SIAM Journal on Scientific and Statistical Computing, Journal Name: SIAM Journal on Scientific and Statistical Computing Journal Issue: 1 Vol. 3; ISSN 2168-3417; ISSN 0196-5204
Publisher:
Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
Country of Publication:
United States
Language:
English

References (5)

A mimmax theory for overdamped systems journal January 1964
Vibrations of Rotating Circumferentially Periodic Structures journal January 1981
Algorithms for the Nonlinear Eigenvalue Problem journal September 1973
The Combination Shift $QZ$ Algorithm journal December 1975
Solving Sparse Symmetric Generalized Eigenvalue Problems without Factorization journal February 1981

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Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
EIGENVALUES
EIGENVECTORS
MATHEMATICAL LOGIC
MATRICES