A QZ-method based on semiseparable matrices

Authors:
Yvette Vanberghen;Raf Vandebril;Marc Van Barel
Affiliations:
K.U.Leuven, Department of Computer Science, Celestijnenlaan 200A, 3001 Heverlee (Leuven), Belgium;K.U.Leuven, Department of Computer Science, Celestijnenlaan 200A, 3001 Heverlee (Leuven), Belgium;K.U.Leuven, Department of Computer Science, Celestijnenlaan 200A, 3001 Heverlee (Leuven), Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 4
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On the convergence properties of the orthogonal similarity transformations to tridiagonal and semiseparable (plus diagonal) form

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Abstract

This manuscript focusses on an alternative method for computing the eigenvalues of a pencil of two matrices, based on semiseparable matrices. An effective reduction of a matrix pair to lower semiseparable, upper triangular form will be presented as well as a QZ-iteration for this matrix pair. Important to remark is that this reduction procedure also inherits a kind of nested subspace iteration as was the case when solving the standard eigenvalue problem with semiseparable matrices. It will also be shown, that the QZ-iteration for a semiseparable-triangular matrix pair is closely related to the QZ-iteration for a Hessenberg-triangular matrix pair.