V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 8. The $RP$-$q$ method and its applications”, Computational methods and algorithms. Part XIX, Zap. Nauchn. Sem. POMI, 334, POMI, St. Petersburg, 2006, 149–164; J. Math. Sci. (N. Y.), 141:6 (2007), 1654

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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 334, Pages 149–164 (Mi znsl229)

This article is cited in 1 scientific paper (total in 2 paper)

To solving multiparameter problems of algebra. 8. The $RP$-$q$ method and its applications

V. N. Kublanovskaya

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

Full-text PDF (212 kB) Citations (2)

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Abstract: A new method (the $RP$-$q$ method) for factorizing scalar polynomials in $q$ variables and $q$-parameter polynomial matrices $(q\ge1)$ of full rank is suggested. Applications of the algorithm to solving systems of nonlinear algebraic equations and some spectral problems for a $q$-parameter polynomial matrix $F$ (such as separation of the eigenspectrum and mixed spectrum of $F$, computation of bases with prescribed spectral properties of the null-space of polynomial solutions of $F$, and computation of the hereditary polynomials of $F$) are considered.

Received: 09.03.2006

English version:
Journal of Mathematical Sciences (New York), 2007, Volume 141, Issue 6, Pages 1654–1662
DOI: https://doi.org/10.1007/s10958-007-0075-8

Bibliographic databases:

UDC: 519

Language: Russian

Citation: V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 8. The $RP$-$q$ method and its applications”, Computational methods and algorithms. Part XIX, Zap. Nauchn. Sem. POMI, 334, POMI, St. Petersburg, 2006, 149–164; J. Math. Sci. (N. Y.), 141:6 (2007), 1654–1662

Citation in format AMSBIB

\Bibitem{Kub06}

\by V.~N.~Kublanovskaya

\paper To solving multiparameter problems of algebra.~8. The $RP$-$q$ method and its applications

\inbook Computational methods and algorithms. Part~XIX

\serial Zap. Nauchn. Sem. POMI

\yr 2006

\vol 334

\pages 149--164

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl229}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2270914}

\zmath{https://zbmath.org/?q=an:1172.15303}

\transl

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

\yr 2007

\vol 141

\issue 6

\pages 1654--1662

\crossref{https://doi.org/10.1007/s10958-007-0075-8}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846963570}

Linking options:

https://www.mathnet.ru/eng/znsl229

https://www.mathnet.ru/eng/znsl/v334/p149

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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