V. N. Kublanovskaya, “To solving problems of algebra for two-parameter matrices. 4”, Computational methods and algorithms. Part XXII, Zap. Nauchn. Sem. POMI, 367, POMI, St. Petersburg, 2009, 121–144; J. Math. Sci. (N. Y.), 165:5 (2010), 562

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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 367, Pages 121–144 (Mi znsl3494)

This article is cited in 6 scientific papers (total in 7 papers)

To solving problems of algebra for two-parameter matrices. 4

V. N. Kublanovskaya

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

Full-text PDF (612 kB) Citations (7)

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Abstract: The paper considers applications of the linearization method to computing points of the finite regular and singular spectra of two-parameter polynomial matrices, of pencils of polynomial matrices of general form, and of two-parameter pencils of constant and polynomial matrices.
This method allows one to reduce the solution of the spectral problems mentioned above to the solution of the generalized eigenproblem for regular matrix pencils, which is a classical algebraic problem.
Also the linearization method is applied to computing the zeros of a polynomial in two variables and the common zeros of a sequence of polynomials in two variables. Bibl. – 3 titles.

Received: 25.02.2009

English version:
Journal of Mathematical Sciences (New York), 2010, Volume 165, Issue 5, Pages 562–573
DOI: https://doi.org/10.1007/s10958-010-9826-z

Bibliographic databases:

UDC: 519

Language: Russian

Citation: V. N. Kublanovskaya, “To solving problems of algebra for two-parameter matrices. 4”, Computational methods and algorithms. Part XXII, Zap. Nauchn. Sem. POMI, 367, POMI, St. Petersburg, 2009, 121–144; J. Math. Sci. (N. Y.), 165:5 (2010), 562–573

Citation in format AMSBIB

\Bibitem{Kub09}

\by V.~N.~Kublanovskaya

\paper To solving problems of algebra for two-parameter matrices.~4

\inbook Computational methods and algorithms. Part~XXII

\serial Zap. Nauchn. Sem. POMI

\yr 2009

\vol 367

\pages 121--144

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl3494}

\transl

\jour J. Math. Sci. (N. Y.)

\yr 2010

\vol 165

\issue 5

\pages 562--573

\crossref{https://doi.org/10.1007/s10958-010-9826-z}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77949280448}

Linking options:

https://www.mathnet.ru/eng/znsl3494

https://www.mathnet.ru/eng/znsl/v367/p121

Cycle of papers

To solving problems of algebra for two-parameter polynomial matrices. 1
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2008, 359, 107–149
To solving problems of algebra for two-parameter matrices. 2
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2008, 359, 150–165
To solving problems of algebra for two-parameter matrices. 3
V. N. Kublanovskaya, V. B. Khazanov
Zap. Nauchn. Sem. POMI, 2008, 359, 166–207
To solving problems of algebra for two-parameter matrices. 4
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2009, 367, 121–144
To solving problems of algebra for two-parameter matrices. 5
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2009, 367, 145–170
To solving problems of algebra for two-parameter matrices. 6
V. N. Kublanovskaya, V. B. Khazanov
Zap. Nauchn. Sem. POMI, 2009, 367, 171–186
To solving problems of algebra for two-parameter matrices. 7
V. N. Kublanovskaya, V. B. Khazanov
Zap. Nauchn. Sem. POMI, 2010, 382, 141–149
To solving problems of algebra for two-parameter matrices. 8
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2010, 382, 150–167
To solving problems of algebra for two-parameter matrices. 9
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2011, 395, 124–141
To solving problems of algebra for two-parameter matrices. 10
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2012, 405, 170–185

This publication is cited in the following 7 articles:

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	276
Full-text PDF :	49
References:	43

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