On convergence of a new secant-like method for solving nonlinear equations |
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Authors: | Hongmin Ren Qingbiao Wu |
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Affiliation: | a Department of Information and Electronics, Hangzhou Radio and TV University, Hangzhou 310012, Zhejiang, PR China b Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China |
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Abstract: | In this paper, we prove that the order of a new secant-like method presented recently with the so-called order of 2.618 is only 2.414. Some mistakes in the derivation leading to such a conclusion are pointed out. Meanwhile, under the assumption that the second derivative of the involved function is bounded, the convergence radius of the secant-like method is given, and error estimates matching its convergence order are also provided by using a generalized Fibonacci sequence. |
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Keywords: | Iterative method Secant-like method Convergence order Error estimate Generalized Fibonacci sequence |
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