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Preprint 738-2002

Jacobi-like algorithms for the indefinite generalized Hermitian eigenvalue problem

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Author(s) : Christian Mehl

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 738-2002

MSC 2000

65F15 Eigenvalues, eigenvectors

Abstract :
We discuss structure-preserving Jacobi-like algorithms for the solution of the indefinite generalized Hermitian eigenvalue problem. We discuss a method based on the solution of Hermitian 4-by-4 subproblems which generalizes the Jacobi-like method of Bunse-Gerstner/Faßbender for Hamiltonian matrices. Furthermore, we discuss structure-preserving Jacobi-like methods based on the solution of non-Hermitian 2-by-2 subproblems. For these methods a local convergence proof is given. Numerical test results for the comparison of the proposed methods are presented.

Keywords : Jacobi-like method, Hermitian pencil, eigenvalues

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