East Asian mathematical journal

  • 제26권3호
  • /
  • Pages.351-363
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  • 2010
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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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)
  • 투고 : 2009.05.13
  • 심사 : 2010.05.12
  • 발행 : 2010.05.31
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초록

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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참고문헌

  1. I. K. Argyros, On the Newton-Kantorovich hypothesis for solving equations, J. Comput. Appl. Math. 169 (2004), 315-332. https://doi.org/10.1016/j.cam.2004.01.029
  2. I. K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004), 374-397. https://doi.org/10.1016/j.jmaa.2004.04.008
  3. I. K. Argyros, Convergence and applications of Newton-type iterations, Springer-Verlag Pub.,New York, 2008.
  4. I. K. Argyros, On a class of Newton-like methods for solving nonlinear equations, J. Comput.Appl. Math. 228 (2009), 115-122. https://doi.org/10.1016/j.cam.2008.08.042
  5. J. E. Dennis, Toward a unied convergence theory for Newton-like methods, in Nonlin-ear Functional Analysis and Applications (L.B. Rall, ed.), Academic Press, New York, (1971), 425-472.
  6. L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982.
  7. J. M. McNamee, Numerical methods for roots of polynomials, part I, 14, Elsevier, 2007.
  8. F. A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Mathe-matica 5 (1985), 71-84.
  9. T. Yamamoto, A convergence theorem for Newton-like methods in Banach spaces, Nu-mer. Math. 51 (1987), 545-557. https://doi.org/10.1007/BF01400355