Author(s)

Shunji Horiguchi

Department of Economics, Niigata Sangyo University, Niigata, Japan.

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

Recurrence Formula, Newton’s Method, Halley’s Method, Extension of Halley’s Method, Third-Order Convergence

Horiguchi, S. (2016) The Convergences Comparison between the Halley’s Method and Its Extended One Based on Formulas Derivation and Numerical Calculations. Applied Mathematics, 7, 2394-2410. doi: 10.4236/am.2016.718188.