An optimal Steffensen-type family for solving nonlinear equations

An optimal Steffensen-type family for solving nonlinear equations

0.00 Avg rating0 Votes
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: , ,
Keywords: programming: nonlinear
Abstract:

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 m evaluations per iteration without memory would arrive at the optimal convergence of order 2 m‐1. Its error equations and asymptotic convergence constants are obtained. Finally, it is compared with the related methods for solving nonlinear equations in the numerical examples.

Reviews

Required fields are marked *. Your email address will not be published.