Geodesic
To solving spectral problems for $q$-parameter polynomial matrices. 2
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIV, Tome 395 (2011), pp. 162-171 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper continues the studies of the method of hereditary pencils for computing points of the finite spectrum of a multiparameter polynomial matrix. The method involves induction on the number of parameters and consists of two stages. At the first stage, given the coefficients of a multiparameter matrix, a sequence of $(q-k)$-parameter polynomial matrices ($k=1,\dots,q$) satisfying certain recursive relations is formed. This sequence is used at the second stage. As the base case, two-parameter matrices and their spectral characteristics, which are computed by applying the method of hereditary pencils, are considered. Algorithms implementing the second stage are suggested and theoretically justified. 
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V. N. Kublanovskaya; V. B. Khazanov. To solving spectral problems for $q$-parameter polynomial matrices. 2. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIV, Tome 395 (2011), pp. 162-171. http://geodesic.mathdoc.fr/item/ZNSL_2011_395_a13/

[1] V. N. Kublanovskaya, “K resheniyu spektralnykh zadach dlya $q$-parametricheskikh polinomialnykh matrits”, Zap. nauchn. semin. POMI, 382, 2010, 168–183

[2] V. N. Kublanovskaya, “K resheniyu zadach algebry dlya dvukhparametrichekskikh matrits. 8”, Zap. nauchn. semin. POMI, 382, 2010, 150–167

[3] V. N. Kublanovskaya, “K resheniyu zadach algebry dlya dvukhparametricheskikh matrits. 9”, Zap. nauchn. semin. POMI, 395, 2011, 124–141

[4] V. N. Kublanovskaya, V. B. Khazanov, Chislennye metody resheniya parametricheskikh zadach algebry. {rm Chast 1.} Odnoparametricheskie zadachi, Nauka, S.-Peterburg, 2004