To solving multiparameter problems of algebra. 2.~The method of partial relative factorization and its applications
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 89-107

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For a $q$-parameter ($q\ge2$) polynomial matrix of full rank whose regular and singular spectra have no points in common, a method for computing its partial relative factorization into a product of two matrices with disjoint spectra is suggested. One of the factors is regular and is represented as a product of $q$ matrices with disjoint spectra. The spectrum of each of the factors is independent of one of the parameters and forms in the space $\mathbb C^q$ a cylindrical manifold w.r.t. this parameter. The method is applied to computing zeros of the minimal polynomial with the corresponding eigenvectors. An application of the method to computing a basis of the null-space of polynomial solutions of the matrix that contains no zeros of its minimal polynomial is considered.
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     author = {V. N. Kublanovskaya},
     title = {To solving multiparameter problems of algebra. {2.~The} method of partial relative factorization and its applications},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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V. N. Kublanovskaya. To solving multiparameter problems of algebra. 2.~The method of partial relative factorization and its applications. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 89-107. http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a5/