Extended Semi-Local Convergence of Newton`s Method using the Center Lipschitz Condition and the Restricted Convergence Domain

Authors : IIoannis K Argyros, Santhosh GEORGE

Pages : 5-9

Doi:10.33401/fujma.503716

View : 22 | Download : 10

Publication Date : 2019-06-17

Article Type : Research Paper

Abstract :The objective of this study is to extend the usage of Newton`s method for Banach space valued operators. We use our new idea of restricted convergence domain in combination with the center Lipschitz hypothesis on the Frechet-derivatives where the center is not necessarily the initial point. This way our semi-local convergence analysis is tighter than in earlier works insert ignore into journalissuearticles values(since the new majorizing function is at least as tight as the ones used before); leading to weaker criteria, better error bounds more precise information on the solution. These improvements are obtained under the same computational effort.
Keywords : Newton`s method, Banach space, Center Lipschitz condition, Semi local convergence