A QZ-method based on semiseparable matrices

Yvette Vanberghen, Raf Vandebril, Marc Van Barel
2008 Journal of Computational and Applied Mathematics  
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
more » ... 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.
doi:10.1016/j.cam.2007.07.032 fatcat:ewqojoz2nzhxlfrgfk7arq7zda