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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 alsodoi:10.1016/j.cam.2007.07.032 fatcat:ewqojoz2nzhxlfrgfk7arq7zda