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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 373, Pages 189–193 (Mi znsl3582)  
This article is cited in 1 scientific paper (total in 1 paper)

Root-squaring with DPR1 matrices

V. Y. Pan

Department of Mathematics and Computer Science Lehman College of the City University of New York Bronx, USA
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Abstract: Recent progress in polynomial root-finding relies on employing the associated companion and generalized companion DPR1 matrices. (“DPR1” stands for “diagonal plus rank-one.”) We propose an algorithm that uses nearly linear arithmetic time to square a DPR1 matrix. Consequently the algorithm squares the roots of the associated characteristic polynomial. This incorporates the classical techniques of polynomial root-finding by means of root-squaring into new effective framework. Our approach is distinct from the earlier fast methods for squaring companion matrices. Bibl. – 13 titles.
Key words and phrases: polynomial root-squaring, DPR1 matrices.
Received: 11.09.2009
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 168, Issue 3, Pages 417–419
DOI: https://doi.org/10.1007/s10958-010-9993-y
Bibliographic databases:
Document Type: Article
UDC: 519.61
Language: English
Citation: V. Y. Pan, “Root-squaring with DPR1 matrices”, Representation theory, dynamical systems, combinatorial methods. Part XVII, Zap. Nauchn. Sem. POMI, 373, POMI, St. Petersburg, 2009, 189–193; J. Math. Sci. (N. Y.), 168:3 (2010), 417–419
Citation in format AMSBIB
\Bibitem{Pan09}
\by V.~Y.~Pan
\paper Root-squaring with DPR1 matrices
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XVII
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 373
\pages 189--193
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3582}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 168
\issue 3
\pages 417--419
\crossref{https://doi.org/10.1007/s10958-010-9993-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77954760916}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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