V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 3. Cylindrical manifolds of the regular spectrum of a matrix”, Computational methods and algorithms. Part XVI, Zap. Nauchn. Sem. POMI, 296, POMI, St. Petersburg, 2003, 108–121; J. Math. Sci. (N. Y.), 127:3 (2005), 2016

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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 296, Pages 108–121 (Mi znsl1233)

To solving multiparameter problems of algebra. 3. Cylindrical manifolds of the regular spectrum of a matrix

V. N. Kublanovskaya

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

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Abstract: Methods for computing polynomials (complete polynomials) whose zeros form in the space $\mathbb C^q$ cylindrical manofolds of the regular spectrum of a $q$-parameter polynomial matrix are considered. Based on the method of partial relative factorization of matrices, new methods for computing cylindrical manifolds are suggested. The $\Psi W$ and $\Psi V$ methods, previously proposed for computing complete polynomials of $q$-parameter polynomial matrices whose regular spectrum is independent of one of the parameters, are extended to a wider class of matrices.

Received: 27.02.2003

English version:
Journal of Mathematical Sciences (New York), 2005, Volume 127, Issue 3, Pages 2016–2023
DOI: https://doi.org/10.1007/s10958-005-0159-2

Bibliographic databases:

UDC: 519

Language: Russian

Citation: V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 3. Cylindrical manifolds of the regular spectrum of a matrix”, Computational methods and algorithms. Part XVI, Zap. Nauchn. Sem. POMI, 296, POMI, St. Petersburg, 2003, 108–121; J. Math. Sci. (N. Y.), 127:3 (2005), 2016–2023

Citation in format AMSBIB

\Bibitem{Kub03}

\by V.~N.~Kublanovskaya

\paper To solving multiparameter problems of algebra. 3.~Cylindrical manifolds of the regular spectrum of a~matrix

\inbook Computational methods and algorithms. Part~XVI

\serial Zap. Nauchn. Sem. POMI

\yr 2003

\vol 296

\pages 108--121

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl1233}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1997196}

\zmath{https://zbmath.org/?q=an:1080.65531}

\transl

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

\yr 2005

\vol 127

\issue 3

\pages 2016--2023

\crossref{https://doi.org/10.1007/s10958-005-0159-2}

Linking options:

https://www.mathnet.ru/eng/znsl1233

https://www.mathnet.ru/eng/znsl/v296/p108

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

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References:	41

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