A modified trust region algorithm for nonlinear equations with new updating rule of trust region radius

Abstract

In this article, we present a trust region algorithm for the nonlinear equations with a new updating rule of the trust region radius, which takes some function of the residual. We show that under the local error bound condition which is weaker than the non-singularity, the new algorithm converges quadratically to some solution of the nonlinear equations. Numerical results show that the new algorithm performs very well for some singular nonlinear equations.

Keywords:

• nonlinear equations
• trust region method
• local error bound condition
• quadratic convergence

2000 AMS Subject Classifications :

• 90C30
• 93E24
• 65K05

Acknowledgements

This work was done when the first author visited the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, supported by the UK/CHINA Postgraduate Research Scholarships, 2006. The first author is also supported by Chinese NSFC grant 10871127, SRF for ROCS, SEM, and Chenxing Program, SJTU. The second author is supported by Chinese NSFC grant 10501013. The authors deeply appreciate the referees for their valuable comments and constructive suggestions, which have greatly improved the original version of the article.