Enclosing roots of polynomial equations and their applications to iterative processes
Journal Title: Surveys in Mathematics and its Applications - Year 2009, Vol 4, Issue 0
Abstract
We introduce a special class of real recurrentpolynomials f<SUB>n</SUB> (n ≥ 1) of degree n,with unique positive roots s<SUB>n</SUB>, which are decreasingas n increases. The first root s<SUB>1</SUB>, as well asthe last one denoted by s<SUB>∞</SUB> are expressed in closedform, and enclose all s<SUB>n</SUB> (n > 1). <BR>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.
Authors and Affiliations
Ioannis Argyros, Saïd Hilout
Keywords
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