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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 6976205, 7 pages
Research Article

The Convergence Ball and Error Analysis of the Relaxed Secant Method

1Department of Mathematics, Taizhou University, Linhai, Zhejiang 317000, China
2Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China
3Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310012, China

Correspondence should be addressed to Qingbiao Wu

Received 4 November 2016; Revised 17 January 2017; Accepted 12 February 2017; Published 8 March 2017

Academic Editor: Kaliyaperumal Nakkeeran

Copyright © 2017 Rongfei Lin 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.


A relaxed secant method is proposed. Radius estimate of the convergence ball of the relaxed secant method is attained for the nonlinear equation systems with Lipschitz continuous divided differences of first order. The error estimate is also established with matched convergence order. From the radius and error estimate, the relation between the radius and the speed of convergence is discussed with parameter. At last, some numerical examples are given.