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Zap. Nauchn. Sem. POMI, 2007, Volume 346, Pages 131–148 (Mi znsl92)  

This article is cited in 1 scientific paper (total in 2 paper)

To solving multiparameter problems of algebra. 11. Computing the regular spectrum of a polynomial matrix

V. N. Kublanovskaya

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: For a general multiparameter polynomial matrix $F(\overline{\lambda})$, solution of the equation $F(\overline{\lambda})x=0$ at points of the finite spectrum of $F(\overline{\lambda})$ is considered. Points of the spectrum of $F(\overline{\lambda})$ are classified in terms of solutions of the determinantal system of nonlinear algebraic equations and also in terms of zeros of certain scalar polynomials (in particular, the characteristic polynomial of the matrix).
Algorithms for computing points of the finite regular spectrum of the matrix with the corresponding vectors are presented.

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English version:
Journal of Mathematical Sciences (New York), 2008, 150:2, 1989–1997

Bibliographic databases:

UDC: 519
Received: 07.05.2007

Citation: V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 11. Computing the regular spectrum of a polynomial matrix”, Computational methods and algorithms. Part XX, Zap. Nauchn. Sem. POMI, 346, POMI, St. Petersburg, 2007, 131–148; J. Math. Sci. (N. Y.), 150:2 (2008), 1989–1997

Citation in format AMSBIB
\Bibitem{Kub07}
\by V.~N.~Kublanovskaya
\paper To solving multiparameter problems of algebra.~11. Computing the regular spectrum of a~polynomial matrix
\inbook Computational methods and algorithms. Part~XX
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 346
\pages 131--148
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl92}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2469445}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2008
\vol 150
\issue 2
\pages 1989--1997
\crossref{https://doi.org/10.1007/s10958-008-0114-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-41149168708}


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    This publication is cited in the following articles:
    1. “To the memory of V. N. Kyblanovskaya”, J. Math. Sci. (N. Y.), 191:1 (2013), 1–3  mathnet  crossref  mathscinet
    2. N. F. Valeev, “Ob odnom spektralnom svoistve irregulyarnykh puchkov”, Ufimsk. matem. zhurn., 4:4 (2012), 45–53  mathnet
  • Записки научных семинаров ПОМИ
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