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The Scientific World Journal
Volume 2014, Article ID 498016, 9 pages
Research Article

On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition

Department of Mathematics and Physics, Quzhou University, Quzhou 324000, China

Received 15 May 2014; Revised 12 August 2014; Accepted 15 August 2014; Published 28 August 2014

Academic Editor: Fazlollah Soleymani

Copyright © 2014 Fangqin Zhou. 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.


We present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the singular systems. It also allows us to obtain an estimate of convergence ball for inexact Newton method and some important special cases.