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http://dx.doi.org/10.7858/eamj.2011.27.3.319

ON THE CONVERGENCE OF INEXACT TWO-STEP NEWTON-TYPE METHODS USING RECURRENT FUNCTIONS  

Argyros, Ioannis K. (Department of Mathematics Sciences Cameron University)
Hilou, Said (Laboratoire de Mathematiques et Application Poitiers University)
Publication Information
East Asian mathematical journal / v.27, no.3, 2011 , pp. 319-337 More about this Journal
Abstract
We approximate a locally unique solution of a nonlinear equation in a Banach space setting using an inexact two-step Newton-type method. It turn out that under our new idea of recurrent functions, our semilocal analysis provides tighter error bounds than before, and in many interesting cases, weaker sufficient convergence conditions. Applications including the solution of nonlinear Chandrasekhar-type integral equations appearing in radiative transfer and two point boundary value problems are also provided in this study.
Keywords
inexact two-step Newton-type method; Banach space; majorizing sequence; semilocal convergence; nonlinear Chandrasekhar-type integral equation; radiative transfer; two point boundary value problems;
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