<![CDATA[This article discusses the Chebyshev-Halley method free from second derivative with one parameter, which is a modification of Chebyshev-Halley method with third order convergence. This method has a convergence of sixth order if the value of theparameter is one and of fifth order if the value of the parameter is other than one. For each iteration of this method, four function evaluations are needed, so that the efficiency index for the parameter is 614 = 1.565. Furthermore, the computational test shows that the discussed method is better than Newton method, Chebyshev method, Halley method, and Super Halley method in terms of the error produced in obtaining the estimated root.]]>
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