Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 4 (2009), 119 -- 132

ENCLOSING ROOTS OF POLYNOMIAL EQUATIONS AND THEIR APPLICATIONS TO ITERATIVE PROCESSES

Ioannis K. Argyros and Saïd Hilout

Abstract. We introduce a special class of real recurrent polynomials fn (n ≥ 1) of degree n, with unique positive roots sn, which are decreasing as n increases. The first root s1, as well as the last one denoted by s∞ are expressed in closed form, and enclose all sn (n > 1).
This technique is also used to find weaker than before [5] sufficient convergence conditions for some popular iterative processes converging to solutions of equations.

2000 Mathematics Subject Classification: 26C10; 12D10; 30C15; 30C10; 65J15; 47J25.
Keywords: real polynomials; enclosing roots; iterative processes; nonlinear equations.

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Ioannis K. Argyros Saïd Hilout
Cameron University, Poitiers University,
Department of Mathematics Sciences, Laboratoire de Mathématiques et Applications,
Lawton, OK 73505, USA. Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179,
e-mail: iargyros@cameron.edu 86962 Futuroscope Chasseneuil Cedex, France.
e-mail: said.hilout@math.univ--poitiers.fr


http://www.utgjiu.ro/math/sma