Improved local analysis for a certain class of iterative methods with cubic convergence

Authors:
Hongmin Ren;Ioannis K. Argyros
Affiliations:
College of Information and Electronics, Hangzhou Polytechnic, Hangzhou, Peoples Republic of China 311402;Department of Mathematical Sciences, Cameron University, Lawton, USA 73505
Venue:
Numerical Algorithms
Year:
2012

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Abstract

We use Lipschitz and center-Lipschitz conditions to provide an improved local convergence analysis for a certain class of iterative methods with cubic order of convergence. It turns out that under the same computational cost as before, we obtain a larger radius of convergence and tighter error bounds. Numerical examples are also provided in this study.