A BFGS algorithm for solving symmetric nonlinear equations

Abstract

In this article, we propose a BFGS method for solving symmetric nonlinear equations. The presented method possesses some favourable properties: (a) the generated sequence of iterates is norm descent; (b) the generated sequence of the quasi-Newton matrix is positive definite and (c) this method possesses the global convergence and superlinear convergence. Numerical results show that the presented method is interesting.

Keywords:

• BFGS method
• nonlinear equations
• global convergence
• superlinear convergence

AMS Subject Classifications::

• 65H10
• 65K05
• 90C26

Acknowledgements

We would like to thank the referees and the editors for giving us many valuable suggestions and comments which improved this article greatly. This work is supported by Program for Excellent Talents in Guangxi Higher Education Institutions, China NSF grands 10761001, and Guangxi SF grands 0991028.