Some variants of Cauchy's method with accelerated fourth-order convergence

Authors:
Jisheng Kou
Affiliations:
Department of Mathematics, Shanghai University, Shanghai 200444, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this paper, we present some variants of Cauchy's method for solving non-linear equations. Analysis of convergence shows that the methods have fourth-order convergence. Per iteration the new methods cost almost the same as Cauchy's method. Numerical results show that the methods can compete with Cauchy's method.