A QZ-method based on semiseparable matrices

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.