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JOURNALS // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics // Archive

Izv. Saratov Univ. Math. Mech. Inform., 2014 Volume 14, Issue 4(1), Pages 428–439 (Mi isu532)

This article is cited in 2 papers

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

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.

UDC: 517.524

DOI: 10.18500/1816-9791-2014-14-4-428-439



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