Open AccessA modified Fletcher-Reeves-Type derivative-free method for symmetric nonlinear equations
Author(s) -
Donghui Li,
Xiaolin Wang
Publication year - 2011
Publication title -
numerical algebra control and optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.303
H-Index - 20
eISSN - 2155-3289
pISSN - 2155-3297
DOI - 10.3934/naco.2011.1.71
Subject(s) - nonlinear system , descent direction , mathematics , line search , descent (aeronautics) , residual , sequence (biology) , derivative (finance) , backtracking , property (philosophy) , local convergence , type (biology) , mathematical analysis , mathematical optimization , algorithm , iterative method , computer science , gradient descent , physics , philosophy , computer security , ecology , financial economics , biology , genetics , epistemology , quantum mechanics , machine learning , artificial neural network , radius , meteorology , economics
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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