A modified Fletcher-Reeves-Type derivative-free  method for symmetric nonlinearequations

Dong-Hui Li; Xiao-Lin Wang

doi:10.3934/naco.2011.1.71

Article Contents

2011, Volume 1, Issue 1: 71-82. Doi: 10.3934/naco.2011.1.71

This issue Previous Article Convergence analysis of sparse quasi-Newton updates with positive definite matrix completion for two-dimensional functions Next Article Celis-Dennis-Tapia based approach to quadratic fractional programming problems with two quadratic constraints

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

Dong-Hui Li^1, and
Xiao-Lin Wang^2,

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

Received: October 2010

Revised: October 2010

Published: January 2011

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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.

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Mathematics Subject Classification: Primary: 65H10; Secondary: 90C30.

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References

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