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2011, 1(1): 71-82. doi: 10.3934/naco.2011.1.71

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

 1 School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China 2 College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

Received  October 2010 Revised  October 2010 Published  February 2011

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.
Citation: Dong-Hui Li, Xiao-Lin Wang. A modified Fletcher-Reeves-Type derivative-free method for symmetric nonlinear equations. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 71-82. doi: 10.3934/naco.2011.1.71
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