Nonmonotone spectral method for large‐scale symmetric nonlinear equations

Nonmonotone spectral method for large‐scale symmetric nonlinear equations

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Article ID: iaor2013602
Volume: 62
Issue: 1
Start Page Number: 149
End Page Number: 162
Publication Date: Jan 2013
Journal: Numerical Algorithms
Authors: ,
Keywords: programming: nonlinear
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.

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