A semi-local convergence theorem for a robust revised Newton's method

Authors:
Zhengyu Wang;Xinyuan Wu
Affiliations:
State Key Laboratory for Novel Software Technology at Nanjing University, Department of Mathematics, Nanjing University, Nanjing 210093, PR China;State Key Laboratory for Novel Software Technology at Nanjing University, Department of Mathematics, Nanjing University, Nanjing 210093, PR China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

It is well known that Newton's iteration will abort due to the overflow if the derivative of the function at an iterate is singular or almost singular. In this paper, we study a robust revised Newton's method for solving nonlinear equations, which can be carried out with a starting point with a degenerate derivative at an iterative step. It is proved that the method is convergent under the conditions of the Newton-Kantorovich theorem, which implies a larger convergence domain of the method. We also show that our method inherits the fast convergence of Newton's method. Numerical experiments are performed to show the robustness of the proposed method in comparison with the standard Newton's method.