Geodesic
To solving multiparameter problems of algebra. 11. Computing the regular spectrum of a polynomial matrix
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 131-148 
V. N. Kublanovskaya. To solving multiparameter problems of algebra. 11. Computing the regular spectrum of a polynomial matrix. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 131-148. http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a9/
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     author = {V. N. Kublanovskaya},
     title = {To solving multiparameter problems of algebra.~11. {Computing} the regular spectrum of a~polynomial matrix},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For a general multiparameter polynomial matrix $F(\overline{\lambda})$, solution of the equation $F(\overline{\lambda})x=0$ at points of the finite spectrum of $F(\overline{\lambda})$ is considered. Points of the spectrum of $F(\overline{\lambda})$ are classified in terms of solutions of the determinantal system of nonlinear algebraic equations and also in terms of zeros of certain scalar polynomials (in particular, the characteristic polynomial of the matrix). Algorithms for computing points of the finite regular spectrum of the matrix with the corresponding vectors are presented.

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