Convergence and Error Estimate of the Steffensen Method

Shang, Xufeng; Shao, Xingping; Wu, Peng

doi:https://doi.org/10.3814/2010/674539

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Research Article | Open Access

Volume 2010 | Article ID 674539 | https://doi.org/10.3814/2010/674539

Convergence and Error Estimate of the Steffensen Method

Xufeng Shang,¹Xingping Shao,²and Peng Wu³

Received15 Jul 2009

Revised30 Aug 2009

Accepted31 Aug 2009

Published28 Sept 2009

Abstract

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.

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Copyright

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.

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