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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 601745, 8 pages
http://dx.doi.org/10.1155/2014/601745
Research Article

Third-Order Newton-Type Methods Combined with Vector Extrapolation for Solving Nonlinear Systems

1Department of Foundation Courses, Hubei Vocational Technical College, Xiaogan, Hubei 432000, China
2School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, Hubei 432000, China

Received 22 March 2014; Accepted 31 May 2014; Published 15 June 2014

Academic Editor: Vinay Kanwar

Copyright © 2014 Wen Zhou and Jisheng Kou. 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

We present a third-order method for solving the systems of nonlinear equations. This method is a Newton-type scheme with the vector extrapolation. We establish the local and semilocal convergence of this method. Numerical results show that the composite method is more robust and efficient than a number of Newton-type methods with the other vector extrapolations.