Horiguchi, S (2016) The Formulas to Compare the Convergences of Newton’s Method and the Extended Newton’s Method (Tsuchikura-Horiguchi Method) and the Numerical Calculations. Applied Mathematics, 7, 40-60.
https://doi.org/10.4236/am.2016.71004

has been cited by the following article:

• 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.