Geodesic
Spectral problem for polynomial matrix pencils. 2
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part V, Tome 111 (1981), pp. 109-116 
V. N. Kublanovskaya. Spectral problem for polynomial matrix pencils. 2. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part V, Tome 111 (1981), pp. 109-116. http://geodesic.mathdoc.fr/item/ZNSL_1981_111_a7/
@article{ZNSL_1981_111_a7,
     author = {V. N. Kublanovskaya},
     title = {Spectral problem for polynomial matrix pencils.~2},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {109--116},
     year = {1981},
     volume = {111},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_111_a7/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For an arbitrary polynomial pencil of matrices $A_i$ of dimensions $m\times n$ one presents an algorithm for the computation of the eigenvalues of the regular kernel of the pencil. The algorithm allows to construct a regular pencil having the same eigenvalues as the regular kernel of the initial pencil or (in the case of a dead end termination) allows to pass from the initial pencil to a pencil of smaller dimensions whose regular kernel has the same eigenvalues as the initial pencil. The problem is solved by reducing the obtained pencil to a linear one. For solving the problem in the case of a linear pencil one considers algorithms for pencils of full column rank as well as for completely singular pencils.