Article ID: | iaor20116395 |
Volume: | 217 |
Issue: | 23 |
Start Page Number: | 9592 |
End Page Number: | 9597 |
Publication Date: | Aug 2011 |
Journal: | Applied Mathematics and Computation |
Authors: | Zheng Quan, Li Jingya, Huang Fengxi |
Keywords: | programming: nonlinear |
In this paper, a general family of Steffensen‐type methods with optimal order of convergence for solving nonlinear equations is constructed by using Newton’s iteration for the direct Newtonian interpolation. It satisfies the conjecture proposed by Kung and Traub [H.T. Kung, J.F. Traub, Optimal order of one‐point and multipoint iteration, J. Assoc. Comput. Math. 21 (1974) 634–651] that an iterative method based on