Numerical Algebra, Control and Optimization (NACO)

A modified Fletcher-Reeves-Type derivative-free method for symmetric nonlinear equations

Pages: 71 - 82, Volume 1, Issue 1, March 2011      doi:10.3934/naco.2011.1.71

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Dong-Hui Li - School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China (email)
Xiao-Lin Wang - College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China (email)

Abstract: In this paper, we propose a descent derivative-free method for solving symmetric nonlinear equations. The method is an extension of the modified Fletcher-Reeves (MFR) method proposed by Zhang, Zhou and Li [25] to symmetric nonlinear equations. It can be applied to solve large-scale symmetric nonlinear equations due to lower storage requirement. An attractive property of the method is that the directions generated by the method are descent for the residual function. By the use of some backtracking line search technique, the generated sequence of function values is decreasing. Under appropriate conditions, we show that the proposed method is globally convergent. The preliminary numerical results show that the method is practically effective.

Keywords:  Symmetric nonlinear equations, derivative-free method, descent direction, global convergence.
Mathematics Subject Classification:  Primary: 65H10; Secondary: 90C30.

Received: October 2010;      Revised: October 2010;      Available Online: February 2011.