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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, Volume 14, Issue 4(1), Pages 428–439
DOI: https://doi.org/10.18500/1816-9791-2014-14-4-428-439 (Mi isu532) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Solution of Algebraic Equations by Continuous Fractions of Nikiportsa

V. I. Shmoylova, G. A. Kirichenkob

a Southern Scientific Center of the Russian Academy of Sciences (SSC RAS), 41, Chehova str., Rostov-on-Don, 344006, Russia
b Southern Federal University, 44, Nekrasovsky, Taganrog, 347928, Russia
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DOI: https://doi.org/10.18500/1816-9791-2014-14-4-428-439
Abstract: Provides analytical expressions representing all the roots of a random algebraic equation of $n$-th degree through the coefficients of the initial equation. These formulas consist of two relations infinite Toeplitz determinants, the diagonal elements of which are the coefficients of algebraic equations. For finding complex roots additionally used the method of summation of divergent continued fractions.
Key words: algebraic equations, infinite Toeplitz determinants, $r/\varphi$-algorithm, divergent continuous fractions.
Bibliographic databases:
Document Type: Article
UDC: 517.524
Language: Russian
Citation: V. I. Shmoylov, G. A. Kirichenko, “Solution of Algebraic Equations by Continuous Fractions of Nikiportsa”, Izv. Saratov Univ. Math. Mech. Inform., 14:4(1) (2014), 428–439
Citation in format AMSBIB
\Bibitem{ShmKir14}
\by V.~I.~Shmoylov, G.~A.~Kirichenko
\paper Solution of Algebraic Equations by Continuous Fractions of Nikiportsa
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 4(1)
\pages 428--439
\mathnet{http://mi.mathnet.ru/isu532}
\crossref{https://doi.org/10.18500/1816-9791-2014-14-4-428-439}
\elib{https://elibrary.ru/item.asp?id=22575452}
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    • This publication is cited in the following 1 articles:
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    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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