Affiliation:
1. Veer Surendra Sai University of Technology
Abstract
The present investigation deals with the critical study of the works of Lancaster and Traub, who have developed $n$th root extraction methods of a real number. It is found that their developed methods are equivalent and the particular cases of Halley's and Householder's methods. Again the methods presented by them are easily obtained from simple modifications of Newton's method, which is the extension of Heron's square root iteration formula. Further, the rate of convergency of their reported methods are studied.
Funder
University Grants Commission
Indian Institute of Science Education and Research Kolkata
Publisher
Sociedade Paranaense de Matematica
Reference13 articles.
1. M. S. Bahgat, M. A. Hafiz, Three-step iterative method with 18th order convergence for solving nonlinear equations. Int. J. Pure Appl. Math. 93, 85-94, (2014).
2. Burton, D.M., History of Mathematics. An Introduction , McGraw Hill, 3rd ed., (1923).
3. W. Gander, On Halley’s iteration method. Amer. Math. Monthly 92, 131-134, (1985).
4. M. A. Hafiz, Solving nonlinear equations using steffensen-type methods with optimal order of convergence. Palesteine J. Math. 3, 113-119, (2014).
5. M. A. Hernandez, N. Romero, Letter to the editor, Accelerated convergence in Newton’s method for approximating square roots. J. Comput. Appl. Math. 177, 225-229, (2005).