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2012 Some New Variants of Cauchy's Methods for Solving Nonlinear Equations
Tianbao Liu, Hengyan Li
J. Appl. Math. 2012(SI06): 1-13 (2012). DOI: 10.1155/2012/927450


We present and analyze some variants of Cauchy's methods free from second derivative for obtaining simple roots of nonlinear equations. The convergence analysis of the methods is discussed. It is established that the methods have convergence order three. Per iteration the new methods require two function and one first derivative evaluations. Numerical examples show that the new methods are comparable with the well-known existing methods and give better numerical results in many aspects.


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Tianbao Liu. Hengyan Li. "Some New Variants of Cauchy's Methods for Solving Nonlinear Equations." J. Appl. Math. 2012 (SI06) 1 - 13, 2012.


Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1268.65067
MathSciNet: MR2991588
Digital Object Identifier: 10.1155/2012/927450

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI06 • 2012
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