Geodesic
To solving multiparameter problems of algebra. 5. The $\nabla V$-$q$ factorization algorithm and its applications
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVII, Tome 309 (2004), pp. 144-153 Cet article a éte moissonné depuis la source Math-Net.Ru

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The algorithm of $\nabla V$-factorization suggested earlier for decomposing one- and two-parameter polynomial matrices of full row rank into a product of two matrices (a regular one, whose spectrum coincides with the finite regular spectrum of the original matrix, and a matrix of full row rank, whose singular spectrum coincides with the singular spectrum of the original matrix, whereas the regular spectrum is empty) is extended to the case of $q$-parameter ($q\geqslant1$) polynomial matrices. The algorithm of $\nabla V$-$q$ factorization is described, and its justification and properties for matrices with arbitrary number of parameters are presented. Applications of the algorithm to computing irreducible factorizations of $q$-parameter matrices, to determining a free basis of the null-space of polynomial solutions of the matrix, and to finding matrix divisors corresponding to divisors of its characteristic polynomial are considered. 
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V. N. Kublanovskaya. To solving multiparameter problems of algebra. 5. The $\nabla V$-$q$ factorization algorithm and its applications. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVII, Tome 309 (2004), pp. 144-153. http://geodesic.mathdoc.fr/item/ZNSL_2004_309_a7/

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