A One-step Steffensen-type Method with Super-cubic Convergence for Solving Nonlinear Equations1 | Zendy

Zhongli Liu | Zendy; Quan Zheng | Zendy

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A One-step Steffensen-type Method with Super-cubic Convergence for Solving Nonlinear Equations1

Author(s) -

Zhongli Liu,

Quan Zheng

Publication year - 2014

Publication title -

procedia computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.334

H-Index - 76

ISSN - 1877-0509

DOI - 10.1016/j.procs.2014.05.171

Subject(s) - steffensen's method , computer science , convergence (economics) , nonlinear system , type (biology) , mathematics , function (biology) , newton's method , order (exchange) , algorithm , point (geometry) , derivative (finance) , local convergence , mathematical optimization , newton's method in optimization , iterative method , geometry , ecology , physics , finance , quantum mechanics , evolutionary biology , financial economics , economics , biology , economic growth

In this paper, a one-step Steffensen-type method of order 3.383 is designed and proved for solving nonlinear equations. This super-cubic convergence is obtained by self-accelerating second-order Steffensen's method twice with memory, but without any new function evaluations. The proposed method is very efficient and convenient, since it is still a derivative-free two-point method. Numerical examples confirm the theoretical results and high computational efficiency

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