The solution of spectral problems for polynomial matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 122-138
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For polynomial matrices of full rank, including matrices of the form $A-\lambda I$ and $A-\lambda B$, numerical methods for solving the following problems are suggested: find the divisors of a polynomial matrix whose spectra coincide with the roots 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 $\Delta W$ and $\Delta V$ factorizations of polynomial matrices. Applications of these methods to the solution of certain algebraic problems are considered.
@article{ZNSL_2003_296_a7,
author = {V. N. Kublanovskaya},
title = {The solution of spectral problems for polynomial matrices},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {122--138},
year = {2003},
volume = {296},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a7/}
}
V. N. Kublanovskaya. The solution of spectral problems for polynomial matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 122-138. http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a7/
[1] V. N. Kublanovskaya, “Rank division algorithms and their applications”, J. Numer. Algebra Appl., 1:2 (1992), 198–213 | MR
[2] V. N. Kublanovskaya, “Metody i algoritmy resheniya spektralnykh zadach dlya polinomialnykh i ratsionalnykh matrits”, Zap. nauchn. semin. POMI, 238, 1997, 7–328 | MR | Zbl
[3] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1988 | MR | Zbl