V. N. Kublanovskaya, “To solving multiparameter problems of algebra 1. Methods for computing complete polynomials and their applications”, Computational methods and algorithms. Part XV, Zap. Nauchn. Sem. POMI, 284, POMI, St. Petersburg, 2002, 143–162; J. Math. Sci. (N. Y.), 121:4 (2004), 2519

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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 284, Pages 143–162 (Mi znsl1542)

This article is cited in 4 scientific papers (total in 5 papers)

To solving multiparameter problems of algebra 1. Methods for computing complete polynomials and their applications

V. N. Kublanovskaya

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

Full-text PDF (238 kB) Citations (5)

Abstract: The notion of a complete polynomial of a multiparameter polynomial matrix, generalizing that of an invariant polynomial of a one-parameter polynomial matrix, is introducted. Methods for computing complete polynomials are suggested. Applications of these methods to various spectral problems for polynomial matrices are considered.

Received: 04.02.2002

English version:
Journal of Mathematical Sciences (New York), 2004, Volume 121, Issue 4, Pages 2519–2529
DOI: https://doi.org/10.1023/B:JOTH.0000026289.67486.26

Bibliographic databases:

UDC: 519

Language: Russian

Citation: V. N. Kublanovskaya, “To solving multiparameter problems of algebra 1. Methods for computing complete polynomials and their applications”, Computational methods and algorithms. Part XV, Zap. Nauchn. Sem. POMI, 284, POMI, St. Petersburg, 2002, 143–162; J. Math. Sci. (N. Y.), 121:4 (2004), 2519–2529

Citation in format AMSBIB

\Bibitem{Kub02}

\by V.~N.~Kublanovskaya

\paper To solving multiparameter problems of algebra 1.~Methods for computing complete polynomials and their applications

\inbook Computational methods and algorithms. Part~XV

\serial Zap. Nauchn. Sem. POMI

\yr 2002

\vol 284

\pages 143--162

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl1542}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1915079}

\zmath{https://zbmath.org/?q=an:1071.65053}

\transl

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

\yr 2004

\vol 121

\issue 4

\pages 2519--2529

\crossref{https://doi.org/10.1023/B:JOTH.0000026289.67486.26}

Linking options:

https://www.mathnet.ru/eng/znsl1542

https://www.mathnet.ru/eng/znsl/v284/p143

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 5 articles:

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

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