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

Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic $\lambda $-matrix$M\lambda ^2 + C\lambda + K$. $M$, $C$ and $K$ are assumed to have special symmetrytype properties which insure that theory analogous to the standard symmetric eigenprob...

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Bibliographic Details
Published inSIAM journal on scientific and statistical computing Vol. 3; no. 1; pp. 58 - 67
Main Authors Scott, David S., Ward, Robert C.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.03.1982
Subjects
Algorithms
Approximation
Eigenvalues
Eigenvectors
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Summary:Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic $\lambda $-matrix$M\lambda ^2 + C\lambda + K$. $M$, $C$ and $K$ are assumed to have special symmetrytype 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.
ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0903005