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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 716019, 9 pages
http://dx.doi.org/10.1155/2014/716019
Research Article

A Limited Memory BFGS Method for Solving Large-Scale Symmetric Nonlinear Equations

College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China

Received 21 June 2014; Accepted 14 July 2014; Published 5 August 2014

Academic Editor: Gonglin Yuan

Copyright © 2014 Xiangrong Li et al. 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

A limited memory BFGS (L-BFGS) algorithm is presented for solving large-scale symmetric nonlinear equations, where a line search technique without derivative information is used. The global convergence of the proposed algorithm is established under some suitable conditions. Numerical results show that the given method is competitive to those of the normal BFGS methods.