Abstract
The algorithm of ∇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 ≥ 1) polynomial matrices. The algorithm of ∇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 a matrix, and to finding matrix divisors corresponding to divisors of its characteristic polynomial are considered. Bibliogrhaphy: 4 titles.
Similar content being viewed by others
REFERENCES
V. N. Kublanovskaya, “An approach to solving multiparameter problems,” Zap. Nauchn. Semin. POMI, 229, 191–246 (1995).
V. N. Kublanovskaya, “Methods and algorithms for solving spectral problems for polynomial and rational matrices,” Zap. Nauchn. Semin. POMI, 238, 3–329 (1997).
V. N. Kublanovskaya, “Rank division algorithms and their applications,” J. Numer. Linear Algebra Appl., 1, No.2, 199–213 (1992).
V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 4,” Zap. Nauchn. Semin. POMI, 309, 127–143 (2004).
V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 2,” Zap. Nauchn. Semin. POMI, 296, 89–107 (2003).
Author information
Authors and Affiliations
Additional information
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 309, 2004, pp. 144–153.
Rights and permissions
About this article
Cite this article
Kublanovskaya, V.N. To Solving Multiparameter Problems of Algebra. 5. The ∇V-q Factorization Algorithm and its Applications. J Math Sci 132, 224–228 (2006). https://doi.org/10.1007/s10958-005-0490-7
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10958-005-0490-7