A variant of Chebyshev’s method with sixth-order convergence |
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| Authors: | Jisheng Kou Yitian Li |
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| Institution: | (1) State Key Laboratory of Water Resources and Hydropower Engineering Sciences, Wuhan University, Wuhan, 430072, China;(2) Department of Mathematics, Shanghai University, Shanghai, 200444, China |
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| Abstract: | In this paper, we present a new variant of Chebyshev’s method for solving non-linear equations. Analysis of convergence shows
that the new method has sixth-order convergence. Per iteration the new method requires two evaluations of the function, one
of its first derivative and one of its second derivative. Thus the efficiency, in term of function evaluations, of the new
method is better than that of Chebyshev’s method. Numerical examples verifying the theory are given.
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| Keywords: | Chebyshev’ s method non-linear equations root-finding iterative method |
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