Article ID: | iaor2014779 |
Volume: | 66 |
Issue: | 1 |
Start Page Number: | 33 |
End Page Number: | 48 |
Publication Date: | May 2014 |
Journal: | Numerical Algorithms |
Authors: | Wang Xiuhua, Kou Jisheng |
Keywords: | Chebyshev |
In this paper, we focus on a family of modified Chebyshev methods and study the semilocal convergence for these methods. Different from the results in reference (Hernández and Salanova, J., 2000), the Hölder continuity of the second derivative is replaced by its generalized continuity condition, and the latter is weaker than the former. Using the recurrence relations, we establish the semilocal convergence of these methods and prove a convergence theorem to show the existence-uniqueness of the solution. The