A Note on the Singh Six-order Variant of Newton’s Method
Marciniak A. 1*,2, Wolf Marek 3
1 Poznan University of Technology, Institute of Computing Science
Piotrowo 2, 60-965 Poznań, Poland
*E-mail: Andrzej.Marciniak@put.poznan.pl2 Higher Vocational State School in Kalisz, Department of Computer Science
Poznanska 201-205, 62-800, Kalisz, Poland3 Cardinal Stefan Wyszynski University
Faculty of Mathematics and Natural Sciences, College of Sciences
ul. Wóycickiego 1/3, Auditorium Maximum, (room 113)
PL-01-938 Warsaw, Poland
E-mail: m.wolf@uksw.edu.pl
Received:
Received: 08 January 2014; revised: 18 November 2015; accepted: 19 November 2015; published online: 29 December 2015
DOI: 10.12921/cmst.2015.21.04.c01
Abstract:
In 2009 in this journal it was published the paper of M. K. Singh [1], in which the author presented a six-order variant of Newton’s method. Unfortunately, in this paper there were a number of printer errors and a serious error in the proof of theorem on the order of the method proposed. Therefore, we have opted for presenting the correct proof of this theorem.
Key words:
iterative methods, Newton's method, nonlinear equations, order of convergence
References:
[1] M. K. Singh, A Six-order Variant of Newton’s Method for
Solving Nonlinear Equations, Computational Methods in
Science and Technology 15(2), 185-193 (2009).
In 2009 in this journal it was published the paper of M. K. Singh [1], in which the author presented a six-order variant of Newton’s method. Unfortunately, in this paper there were a number of printer errors and a serious error in the proof of theorem on the order of the method proposed. Therefore, we have opted for presenting the correct proof of this theorem.
Key words:
iterative methods, Newton's method, nonlinear equations, order of convergence
References:
[1] M. K. Singh, A Six-order Variant of Newton’s Method for
Solving Nonlinear Equations, Computational Methods in
Science and Technology 15(2), 185-193 (2009).
