Computing multiple zeros by using a parameter in Newton-Secant method

Massimiliano Ferrara; Somayeh Sharifi; Mehdi Salimi

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arXiv · 1507.03493

Computing multiple zeros by using a parameter in Newton-Secant method

Massimiliano Ferrara·Somayeh Sharifi·Mehdi Salimi

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Abstract

In this paper, we modify the Newton-Secant method with third order of convergence for finding multiple roots of nonlinear equations. Per iteration this method requires two evaluations of the function and one evaluation of its first derivative. This method has the efficiency index equal to $3^{\frac{1}{3}}\approx 1.44225$. We describe the analysis of the proposed method along with numerical experiments including comparison with existing methods. Moreover, the dynamics of the proposed method are shown with some comparisons to the other existing methods.

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Massimiliano Ferrara, Somayeh Sharifi, Mehdi Salimi. 2015-07-13. Computing multiple zeros by using a parameter in Newton-Secant method. https://arxiv.org/abs/1507.03493

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