Geodesic
Computation of characteristics of the regular finite spectrum of a singular multiparameter polynomial matrix
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 259-271

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A modification of a known algorithm for computing the generating eigenvectors of a multiparameter polynomial matrix of full column rank is presented. This modification permits one to compute the characteristic polynomial (or its divisors) for a singular matrix. The algorithm proposed can be extended to the general case and used for computing a minimal basis of the image of a polynomial matrix and also for computing the greatest common divisor of scalar and matrix polynomials. An illustration of implementation of the algorithm is given. 
@article{ZNSL_2019_482_a17,
     author = {V. B. Khazanov},
     title = {Computation of characteristics of the regular finite spectrum of a singular multiparameter polynomial matrix},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {259--271},
     publisher = {mathdoc},
     volume = {482},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a17/}
}
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V. B. Khazanov. Computation of characteristics of the regular finite spectrum of a singular multiparameter polynomial matrix. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 259-271. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a17/