Nonmonotone spectral method for large-scale symmetric nonlinear equations

Authors:
Wanyou Cheng;Zixin Chen
Affiliations:
College of Computer, Dongguan University of Technology, Dongguan, China 523808;College of City, Dongguan University of Technology, Dongguan, China 523808
Venue:
Numerical Algorithms
Year:
2013

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Abstract

In this paper, by the use of the residual vector and an approximation to the steepest descent direction of the norm function, we develop a norm descent spectral method for solving symmetric nonlinear equations. The method based on the nomonotone line search techniques is showed to be globally convergent. A specific implementation of the method is given which exploits the recently developed cyclic Barzilai---Borwein (CBB) for unconstrained optimization. Preliminary numerical results indicate that the method is promising.