The convergence ball of the Secant method under Hölder continuous divided differences

Authors:
Ren Hongmin;Wu Qingbiao
Affiliations:
Department of Information and Engineering, Hangzhou Radio and TV University, Hangzhou, Zhejiang, PR China and Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, PR China;Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

Under the hypothesis that nonlinear operators have Hölder continuous divided differences of order one, an estimate of the radius of the convergence ball of the Secant method is obtained, error estimate is also established.