Geodesic
On irreducible factorization of rational matrices and their applications
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part X, Tome 219 (1994), pp. 117-157

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This paper is an extension of the investigation of computational aspects of the spectral problems for a rational matrix from [4]. Methods of the solution of spectral problems for one- and two-parameter rational matrices are considered. The algorithms of constructing irreducible factorizations and among them a minimal factorization by degree and sizes of factors are suggested. Those algorithms allow us to reduce the spectral problems for rational matrices to the same problems for polynomial matrices. A relationship between the irreducible factorization and irreducible realization for a one-parameter matrix and its application in system theory is established. The results are extended to two-parameter rational matrices. Bibliography: 15 titles. 
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     author = {V. N. Kublanovskaya and V. B. Khazanov},
     title = {On irreducible factorization of rational matrices and their applications},
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V. N. Kublanovskaya; V. B. Khazanov. On irreducible factorization of rational matrices and their applications. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part X, Tome 219 (1994), pp. 117-157. http://geodesic.mathdoc.fr/item/ZNSL_1994_219_a5/