Table of Contents
SRX Mathematics
Volume 2010 (2010), Article ID 674539, 5 pages
Research Article

Convergence and Error Estimate of the Steffensen Method

1Department of Mathematics, China Jiliang University, Hangzhou 310018, China
2Department of Mathematics, Zhejiang University, Hangzhou 310027, China
3China Academy of Railway Sciences, Beijing 100081, China

Received 15 July 2009; Revised 30 August 2009; Accepted 31 August 2009

Copyright © 2010 Xufeng Shang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present the Steffensen method in Rn space. The convergence theorem is established by using the technique of majorizing function. Meanwhile, an error estimate is given. It avoids the calculus of derivative but has the same convergence order 2 with Newton's method. Finally, illustrative examples are included to demonstrate the validity and applicability of the technique.