A Steffensen-like method and its higher-order variants |
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Authors: | Quan Zheng Jing Wang Peng Zhao Li Zhang |
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Institution: | College of Sciences, North China University of Technology, Beijing 100144, China |
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Abstract: | For solving nonlinear equations, we suggest a second-order parametric Steffensen-like method, which is derivative free and only uses two evaluations of the function in one step. We also suggest a variant of the Steffensen-like method which is still derivative free and uses four evaluations of the function to achieve cubic convergence. Moreover, a fast Steffensen-like method with super quadratic convergence and a fast variant of the Steffensen-like method with super cubic convergence are proposed by using a parameter estimation. The error equations and asymptotic convergence constants are obtained for the discussed methods. The numerical results and the basins of attraction support the proposed methods. |
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Keywords: | Nonlinear equation Newton&rsquo s method Steffensen method Convergence order Error equation Asymptotic convergence constant Basin of attraction |
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