Nonmonotone spectral methods for large-scale nonlinear systems


This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. The spectral gradient method has proved to be effective for solving large-scale optimization problems. In this work we extend the spectral approach to solve nonlinear systems of equations. We consider a strategy based on nonmonotone line search techniques to guarantee global convergence, and discuss implementation details for solving large-scale problems. We compare the performance of our new method with recent implementations of inexact Newton schemes based on Krylov subspace inner iterative methods for the linear systems. Our numerical experiments indicate that the spectral approach for solving nonlinear systems competes favorably with well-established numerical methods.

DOI: 10.1080/10556780310001610493

Cite this paper

@article{Cruz2003NonmonotoneSM, title={Nonmonotone spectral methods for large-scale nonlinear systems}, author={William La Cruz and Marcos Raydan}, journal={Optimization Methods and Software}, year={2003}, volume={18}, pages={583-599} }