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Byline: V. N. Kublanovskaya (1), V. B. Khazanov (2) Abstract: Properties of the method of IW-q factorization of multiparameter polynomial matrices are analyzed. Modifications of the method, used in solving spectral and other multiparameter problems of algebra, are discussed. Bibliogrhaphy: 11 titles. Author Affiliation: (1) St. Petersburg Department, Steklov Mathematical Institute, St. Petersburg, Russia (2) St. Petersburg Marine Technical University, St. Petersburg, Russia Article History: Registration Date: 22/11/2005 Received Date: 28/05/2004 Article note: Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 309, 2004, pp. 154--165.

Byline: V. N. Kublanovskaya (1) Abstract: The algorithm of aV-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 aY= 1) polynomial matrices. The algorithm of aV-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 a matrix, and to finding matrix divisors corresponding to divisors of its characteristic polynomial are considered. Bibliogrhaphy: 4 titles. Author Affiliation: (1) St. Petersburg Department, Steklov Mathematical Institute, St. Petersburg, Russia Article History: Registration Date: 22/11/2005 Received Date: 04/02/2004 Article note: Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 309, 2004, pp. 144--153.