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http://dx.doi.org/10.14403/jcms.2015.28.1.1

THE CONVERGENCE BALL OF INEXACT NEWTON-LIKE METHOD IN BANACH SPACE UNDER WEAK LIPSHITZ CONDITION  

Argyros, Ioannis K. (Department of Mathematicsal Sciences Cameron University)
George, Santhosh (Department of Mathematical and Computational Sciences NIT Karnataka)
Publication Information
Journal of the Chungcheong Mathematical Society / v.28, no.1, 2015 , pp. 1-12 More about this Journal
Abstract
We present a local convergence analysis for inexact Newton-like method in a Banach space under weaker Lipschitz condition. The convergence ball is enlarged and the estimates on the error distances are more precise under the same computational cost as in earlier studies such as [6, 7, 11, 18]. Some special cases are considered and applications for solving nonlinear systems using the Newton-arithmetic mean method are improved with the new convergence technique.
Keywords
inexact Newton-like method; Banach space; convergence ball; local convergence; weak Lipschitz condition;
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