Geodesic
To the solution of partial eigenproblems for polynomial matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 163-176

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Methods for computing scalar and vector spectral characteristics of a polynomial matrix are proposed. These methods are based on determining the so-called generating vectors (eigenvectors and principal vectors) by using the rank-factorization method for polynomial matrices. The possibility of extending the methods to the case of two-parameter polynomial matrices is indicated. 
@article{ZNSL_2002_284_a9,
     author = {V. N. Kublanovskaya and V. B. Khazanov},
     title = {To the solution of partial eigenproblems for polynomial matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {163--176},
     publisher = {mathdoc},
     volume = {284},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a9/}
}
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V. N. Kublanovskaya; V. B. Khazanov. To the solution of partial eigenproblems for polynomial matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 163-176. http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a9/