V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 2. The method of partial relative factorization and its applications”, Computational methods and algorithms. Part XVI, Zap. Nauchn. Sem. POMI, 296, POMI, St. Petersburg, 2003, 89–107; J. Math. Sci. (N. Y.), 127:3 (2005), 2006

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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 296, Pages 89–107 (Mi znsl1232)

This article is cited in 10 scientific papers (total in 11 papers)

To solving multiparameter problems of algebra. 2. The method of partial relative factorization and its applications

V. N. Kublanovskaya

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

Full-text PDF (229 kB) Citations (11)

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Abstract: For a $q$-parameter ($q\ge2$) polynomial matrix of full rank whose regular and singular spectra have no points in common, a method for computing its partial relative factorization into a product of two matrices with disjoint spectra is suggested. One of the factors is regular and is represented as a product of $q$ matrices with disjoint spectra. The spectrum of each of the factors is independent of one of the parameters and forms in the space $\mathbb C^q$ a cylindrical manifold w.r.t. this parameter. The method is applied to computing zeros of the minimal polynomial with the corresponding eigenvectors. An application of the method to computing a basis of the null-space of polynomial solutions of the matrix that contains no zeros of its minimal polynomial is considered.

Received: 27.02.2003

English version:
Journal of Mathematical Sciences (New York), 2005, Volume 127, Issue 3, Pages 2006–2015
DOI: https://doi.org/10.1007/s10958-005-0158-3

Bibliographic databases:

UDC: 519

Language: Russian

Citation: V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 2. The method of partial relative factorization and its applications”, Computational methods and algorithms. Part XVI, Zap. Nauchn. Sem. POMI, 296, POMI, St. Petersburg, 2003, 89–107; J. Math. Sci. (N. Y.), 127:3 (2005), 2006–2015

Citation in format AMSBIB

\Bibitem{Kub03}

\by V.~N.~Kublanovskaya

\paper To solving multiparameter problems of algebra. 2.~The method of partial relative factorization and its applications

\inbook Computational methods and algorithms. Part~XVI

\serial Zap. Nauchn. Sem. POMI

\yr 2003

\vol 296

\pages 89--107

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl1232}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1997195}

\zmath{https://zbmath.org/?q=an:1080.65530}

\transl

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

\yr 2005

\vol 127

\issue 3

\pages 2006--2015

\crossref{https://doi.org/10.1007/s10958-005-0158-3}

Linking options:

https://www.mathnet.ru/eng/znsl1232

https://www.mathnet.ru/eng/znsl/v296/p89

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 11 articles:

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

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Full-text PDF :	91
References:	56

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