%0 Journal Article
%T Enclosing roots of polynomial equations and their applications to iterative processes
%A Ioannis K. Argyros
%A Sa£¿d Hilout
%J Surveys in Mathematics and its Applications
%D 2009
%I University Constantin Brancusi of Targu-Jiu
%X We introduce a special class of real recurrentpolynomials fn (n ¡Ý 1) of degree n,with unique positive roots sn, which are decreasingas n increases. The first root s1, as well asthe last one denoted by s¡Þ are expressed in closedform, and enclose all sn (n > 1). This technique is also used to find weaker than before[Kantorovich and Akilov, 1982] sufficient convergence conditions for some popular iterative processes converging to solutions of equations.
%K Real polynomials
%K Enclosing roots
%K Iterative processes
%K Nonlinear equations.
%U http://www.utgjiu.ro/math/sma/v04/p10.pdf