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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 720640, 2 pages
http://dx.doi.org/10.1155/2013/720640
Letter to the Editor

Comment on “A New Second-Order Iteration Method for Solving Nonlinear Equations”

School of Mechanical, College of Science, Inner Mongolia University of Technology, Hohhot 010051, China

Received 21 May 2013; Accepted 1 September 2013

Academic Editor: Allan Peterson

Copyright © 2013 Haibin Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Kang et al. claimed that they obtained a new iteration formulation for nonlinear algebraic equations; however the “new” formulation was first derived in 2007 by the variational iteration method.


Recently Kang et al. studied the following algebraic equation: and obtained the following iteration formulation [1, Equation ]:

Kang et al. claimed that this was a new iteration formulation [1]; however, a more general iteration formulation has appeared in 2007 [2].

Consider a nonlinear algebraic equation

By the variational iteration method [2], the following iteration formulation was obtained [2, Equation ]: where is an auxiliary function.

Choosing and in (4), we have This is exactly (2).

Using the basic idea of the variational iteration method as illustrated in [2] (see in [2]), we can construct an iteration formulation for (1) in the form where is a Lagrange multiplier. To identify the multiplier, we set (see [2, Equation ]) from which the multiplier can be identified, which is This results in

Remark 1. Equation (9) is exactly (2) or (4) when and .

Remark 2. Equation (7) is exactly equivalent to in [1].

Remark 3. in [1] is exactly equivalent to the Lagrange multiplier in (7).

Remark 4. The derivation process is the same as that given in [2].

It can be concluded that the so-called new iteration method is a special case of He 2007 formulation; various modifications of Newton iteration formulations are available in [27].

References

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