Abstract
For polynomial matrices of full rank, including matrices of the form A - λI and A - λB, numerical methods for solving the following problems are suggested: find the divisors of a polynomial matrix whose spectra coincide with the zeros of known divisors of its characteristic polynomial; compute the greatest common divisor of a sequence of polynomial matrices; solve the inverse eigenvalue problem for a polynomial matrix. The methods proposed are based on the ΔW and ΔV factorizations of polynomial matrices. Applications of these methods to the solution of certain algebraic problems are considered. Bibliography: 3 titles.
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REFERENCES
V. N. Kublanovskaya, “Rank division algorithms and their applications,” J. Numer. Algebra Appl., 2, 198–213 (1992).
V. N. Kublanovskaya, “Methods and algorithms for solving spectral problems for polynomial and rational matrices,” Zap. Nauchn. Semin. POMI, 238, 3–329 (1997).
F. R. Gantmakher, The Theory of Matrices [in Russian], Nauka, Moscow (1988).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 296, 2003, pp. 122–138.
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Kublanovskaya, V.N. Solution of spectral problems for polynomial matrices. J Math Sci 127, 2024–2032 (2005). https://doi.org/10.1007/s10958-005-0160-9
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DOI: https://doi.org/10.1007/s10958-005-0160-9