V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 10. Computing zeros of a scalar polynomial”, Computational methods and algorithms. Part XX, Zap. Nauchn. Sem. POMI, 346, POMI, St. Petersburg, 2007, 119–130; J. Math. Sci. (N. Y.), 150:2 (2008), 1982

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Zapiski Nauchnykh Seminarov POMI, 2007, Volume 346, Pages 119–130 (Mi znsl91)

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

To solving multiparameter problems of algebra. 10. Computing zeros of a scalar polynomial

V. N. Kublanovskaya

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

Full-text PDF (184 kB) Citations (2)

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Abstract: The paper considers the problem of computing zeros of scalar polynomials in several variables. The zeros of a polynomial are subdivided into the regular (eigen- and mixed) zeros and the singular ones. An algorithm for computing regular zeros, based on a decomposition of a given polynomial into a product of primitive polynomials, is suggested. The algorithm is applied to solving systems of nonlinear algebraic equations.

Received: 16.05.2007

English version:
Journal of Mathematical Sciences (New York), 2008, Volume 150, Issue 2, Pages 1982–1988
DOI: https://doi.org/10.1007/s10958-008-0113-1

Bibliographic databases:

UDC: 519

Language: Russian

Citation: V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 10. Computing zeros of a scalar polynomial”, Computational methods and algorithms. Part XX, Zap. Nauchn. Sem. POMI, 346, POMI, St. Petersburg, 2007, 119–130; J. Math. Sci. (N. Y.), 150:2 (2008), 1982–1988

Citation in format AMSBIB

\Bibitem{Kub07}

\by V.~N.~Kublanovskaya

\paper To solving multiparameter problems of algebra.~10.

Computing zeros of a scalar polynomial

\inbook Computational methods and algorithms. Part~XX

\serial Zap. Nauchn. Sem. POMI

\yr 2007

\vol 346

\pages 119--130

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl91}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2469444}

\transl

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

\yr 2008

\vol 150

\issue 2

\pages 1982--1988

\crossref{https://doi.org/10.1007/s10958-008-0113-1}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-41149120004}

Linking options:

https://www.mathnet.ru/eng/znsl91

https://www.mathnet.ru/eng/znsl/v346/p119

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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Abstract page:	289
Full-text PDF :	83
References:	54

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