| Article ID: | iaor20126136 |
| Volume: | 61 |
| Issue: | 3 |
| Start Page Number: | 413 |
| End Page Number: | 427 |
| Publication Date: | Nov 2012 |
| Journal: | Numerical Algorithms |
| Authors: | Gu Chuanqing, Zheng Lin |
| Keywords: | algebra, Banach space |
In this paper, we introduce a new iterative method of order six and study the semilocal convergence of the method by using the recurrence relations for solving nonlinear equations in Banach spaces. We prove an existence‐uniqueness theorem and give a priori error bounds which demonstrates the R‐order of the method to be six. Finally, we give some numerical applications to demonstrate our approach.