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

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Zapiski Nauchnykh Seminarov 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

Full-text PDF (217 kB) Citations (2)

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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.

Received: 07.05.2007

English version:
Journal of Mathematical Sciences (New York), 2008, Volume 150, Issue 2, Pages 1989–1997
DOI: https://doi.org/10.1007/s10958-008-0114-0

Bibliographic databases:

UDC: 519

Language: Russian

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://mathscinet.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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-41149168708}

Linking options:

https://www.mathnet.ru/eng/znsl92

https://www.mathnet.ru/eng/znsl/v346/p131

Cycle of papers

To solving multiparameter problems of algebra 1. Methods for computing complete polynomials and their applications
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2002, 284, 143–162
To solving multiparameter problems of algebra. 2. The method of partial relative factorization and its applications
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2003, 296, 89–107
To solving multiparameter problems of algebra. 3. Cylindrical manifolds of the regular spectrum of a matrix
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2003, 296, 108–121
To solving multiparameter problems of algebra. 4. The $AB$-algorithm and its applications
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2004, 309, 127–143
To solving multiparameter problems of algebra. 5. The $\nabla V$-$q$ factorization algorithm and its applications
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2004, 309, 144–153
To solving multiparameter problems of algebra. 6. Spectral characteristics of polynomial matrices
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2005, 323, 132–149
To solving multiparameter problems of algebra. 7. The $PG$-$q$ factorization method and its applications
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2005, 323, 150–163
To solving multiparameter problems of algebra. 8. The $RP$-$q$ method and its applications
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2006, 334, 149–164
To solving multiparameter problems of algebra. 9. The $\Psi F$-$q$ method for factorizing invariant polynomials and its applications
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2006, 334, 165–173
To solving multiparameter problems of algebra. 10. Computing zeros of a scalar polynomial
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2007, 346, 119–130
To solving multiparameter problems of algebra. 11. Computing the regular spectrum of a polynomial matrix
V. N. Kublanovskaya
Zap. Nauchn. Sem. POMI, 2007, 346, 131–148

This publication is cited in the following 2 articles:

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

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