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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 395, Pages 162–171 (Mi znsl4647)  
This article is cited in 2 scientific papers (total in 3 papers)

To solving spectral problems for $q$-parameter polynomial matrices. 2

V. N. Kublanovskayaa, V. B. Khazanovb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State Marine Technical University, St. Petersburg, Russia
Full-text PDF (551 kB) Citations (3)
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Abstract: The paper continues the studies of the method of hereditary pencils for computing points of the finite spectrum of a multiparameter polynomial matrix. The method involves induction on the number of parameters and consists of two stages. At the first stage, given the coefficients of a multiparameter matrix, a sequence of $(q-k)$-parameter polynomial matrices ($k=1,\dots,q$) satisfying certain recursive relations is formed. This sequence is used at the second stage. As the base case, two-parameter matrices and their spectral characteristics, which are computed by applying the method of hereditary pencils, are considered. Algorithms implementing the second stage are suggested and theoretically justified.
Key words and phrases: regular spectrum, singular spectrum, method of hereditary penils, multiparameter polynomial matrix.
Received: 29.09.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 182, Issue 6, Pages 834–838
DOI: https://doi.org/10.1007/s10958-012-0792-5
Bibliographic databases:
Document Type: Article
UDC: 519
Language: Russian
Citation: V. N. Kublanovskaya, V. B. Khazanov, “To solving spectral problems for $q$-parameter polynomial matrices. 2”, Computational methods and algorithms. Part XXIV, Zap. Nauchn. Sem. POMI, 395, POMI, St. Petersburg, 2011, 162–171; J. Math. Sci. (N. Y.), 182:6 (2012), 834–838
Citation in format AMSBIB
\Bibitem{KubKha11}
\by V.~N.~Kublanovskaya, V.~B.~Khazanov
\paper To solving spectral problems for $q$-parameter polynomial matrices.~2
\inbook Computational methods and algorithms. Part~XXIV
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 395
\pages 162--171
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4647}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2870169}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 182
\issue 6
\pages 834--838
\crossref{https://doi.org/10.1007/s10958-012-0792-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84861766330}
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  • https://www.mathnet.ru/eng/znsl/v395/p162
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    Citing articles in Google Scholar: Russian citations, English citations
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