TITLE:
The Convergences Comparison between the Halley’s Method and Its Extended One Based on Formulas Derivation and Numerical Calculations
AUTHORS:
Shunji Horiguchi
KEYWORDS:
Recurrence Formula, Newton’s Method, Halley’s Method, Extension of Halley’s Method, Third-Order Convergence
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.18,
December
27,
2016
ABSTRACT: 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.