Geodesic
To solving problems of algebra for two-parameter matrices.~7
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIII, Tome 382 (2010), pp. 141-149

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The paper discusses the rank-factorization method for solving spectral problems for two-parameter polynomial matrices. New forms of rank factorization for matrices free of the singular spectrum are suggested. The algorithms for computing them use unimodular matrices only. The paper suggests conditions sufficient for a matrix to have no singular spectrum and also conditions sufficient for a basis matrix of the null-space to have neither the finite regular, nor the finite singular spectrum. Bibl. 3 titles. 
@article{ZNSL_2010_382_a10,
     author = {V. N. Kublanovskaya and V. B. Khazanov},
     title = {To solving problems of algebra for two-parameter matrices.~7},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {141--149},
     publisher = {mathdoc},
     volume = {382},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_382_a10/}
}
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V. N. Kublanovskaya; V. B. Khazanov. To solving problems of algebra for two-parameter matrices.~7. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIII, Tome 382 (2010), pp. 141-149. http://geodesic.mathdoc.fr/item/ZNSL_2010_382_a10/