Copyright © 2009 Gonglin Yuan 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.
A trust-region-based BFGS method is proposed for solving symmetric
nonlinear equations. In this given algorithm, if the trial step is unsuccessful, the
linesearch technique will be used instead of repeatedly solving the subproblem of the
normal trust-region method. We establish the global and superlinear convergence
of the method under suitable conditions. Numerical results show that the given
method is competitive to the normal trust region method.