On preconditioned iterative methods for solving (A−λB)x=0

In this paper a preconditioned iterative method suitable for the solution of the generalized eigenvalue problem is presented. The proposed method in which no change in the structure of the original matrices occurs is suitable for the determination of the extreme eigenvalues and their corresponding e...

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Bibliographic Details
Published inComputing Vol. 32; no. 2; pp. 139 - 152
Main Author Evans, D. J.
Format Journal Article
LanguageEnglish
Published Wien Springer 01.06.1984
Subjects
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Iterative method
Eigenvalue problem
Equation system
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ISSN0010-485X
1436-5057
DOI10.1007/BF02253688

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Summary:In this paper a preconditioned iterative method suitable for the solution of the generalized eigenvalue problem is presented. The proposed method in which no change in the structure of the original matrices occurs is suitable for the determination of the extreme eigenvalues and their corresponding eigenvectors of large sparse matrices derived from finite element/difference discretization of partial differential equations. The new method when coupled with the conjugate gradient algorithm yields a powerful algorithm for this class of problems.
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ISSN:0010-485X
1436-5057
DOI:10.1007/BF02253688