Unified majorizing sequences for Traub-type multipoint iterative procedures

Authors:
I. K. Argyros;D. González
Affiliations:
Department of Mathematical Sciences, Cameron University, Lawton, USA 73505;Department of Mathematics and Computation, University of La Rioja, Logroño, Spain
Venue:
Numerical Algorithms
Year:
2013

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Abstract

We present a unified approach to generating majorizing sequences for multipoint iterative procedures in order to solve nonlinear equations in a Banach space setting. The semilocal convergence results have the following advantages over earlier work (under the same computational cost): weaker sufficient convergence conditions, more precise error bounds on the distances involved and more precise information on the location of the solution. Special cases and numerical examples are also provided in this study.