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http://dx.doi.org/10.7858/eamj.2010.26.3.351

LOCATING ROOTS OF A CERTAIN CLASS OF POLYNOMIALS

Argyros, Ioannis K. (CAMERON UNIVERSITY DEPARTMENT OF MATHEMATICS SCIENCES)
Hilout, Said (POITIERS UNIVERSITY LABORATOIRE DE MATHEMATIQUES ET APPLICATIONS)

Publication Information

East Asian mathematical journal / v.26, no.3, 2010 , pp. 351-363 More about this Journal

Abstract

We introduce a special class of real recurrent polynomials $f_m$$ ( $m{\geq}1$ ) of degree m+1, with positive roots $s_m$ , which are decreasing as m increases. The first root $s_1$ , as well as the last one denoted by $s_{\infty}$ are expressed in closed form, and enclose all $s_m$ (m > 1). This technique is also used to find weaker than before [6] sufficient convergence conditions for some popular iterative processes converging to solutions of equations.

Keywords

real polynomials; enclosing roots; iterative processes; nonlinear equations;

Citations & Related Records

Reference

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