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

Computing multiple zeros by using a parameter in Newton–Secant method In this paper, we modify the Newton–Secant method with third order of convergence for finding multiple roots of nonlinear equations. This method requires two evaluations of the function and one evaluation of its first derivative per iteration. This method has the efficiency index equal to $$3^{\frac{1}{3}}\approx 1.44225$$ 3 1 3 ≈ 1.44225 . We describe the analysis of the proposed method along with numerical experiments including comparison with existing methods. Moreover, the attraction basins of the proposed method are shown and compared with other existing methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SeMA Journal Springer Journals

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

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Publisher
Springer Milan
Copyright
Copyright © 2016 by Sociedad Española de Matemática Aplicada
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
2254-3902
eISSN
2281-7875
D.O.I.
10.1007/s40324-016-0074-0
Publisher site
See Article on Publisher Site

Abstract

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

Journal

SeMA JournalSpringer Journals

Published: Feb 25, 2016

References

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