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Numerical Algorithms

, Volume 62, Issue 1, pp 149–162 | Cite as

Nonmonotone spectral method for large-scale symmetric nonlinear equations

  • Wanyou Cheng
  • Zixin Chen
Original Paper

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.

Keywords

Spectral method Nonmonotone line search Symmetric nonlinear equations 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.College of ComputerDongguan University of TechnologyDongguanChina
  2. 2.College of CityDongguan University of TechnologyDongguanChina

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