East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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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)
  • Received : 2009.05.13
  • Accepted : 2010.05.12
  • Published : 2010.05.31
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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.

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References

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