A QZ-algorithm for semiseparable matrices

This manuscript focusses on the translation of the traditional eigenvalue problem, based on sparse matrices, towards a structured rank approach. An effective reduction of a matrix pair to lower semiseparable, upper triangular form will be presented as well as a QZ-method for this matrix pair. Important to remark is that this reduction procedure also inherits a kind of nested subspace iteration as was the case in the regular eigenvalue problem based on semiseparable matrices. It will also be shown, that the QZ-method for structured rank matrices is closely related to the traditional QZ-method for sparse matrices.nrpages: 17status: publishe