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The Convergences Comparison between the Halley’s Method and Its Extended One Based on Formulas Derivation and Numerical Calculations

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Document pages: 17 pages

Abstract: The purpose of this paper is that we givean extension of Halley’s method (Section 2), and the formulas to compare theconvergences of the Halley’s method and extended one (Section 3). For extensionof Halley’s method we give definition of function by variable transformation inSection 1. In Section 4 we do the numerical calculations of Halley’s method andextended one for elementary functions, compare these convergences, and confirmthe theory. Under certain conditions we can confirm that the extended Halley’smethod has better convergence or better approximation than Halley’s method.

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