Convergence Properties of the Inexact Levenberg-Marquardt Method under Local Error Bound Conditions

2002 ◽  
Vol 17 (4) ◽  
pp. 605-626 ◽  
Author(s):  
Hiroshige Dan ◽  
Nobuo Yamashita ◽  
Masao Fukushima
Keyword(s):  
Error Bound ◽  
Local Error ◽  
Convergence Properties ◽  
Local Error Bound ◽  
Marquardt Method ◽  
Levenberg Marquardt

scholarly journals A New Modified Efficient Levenberg–Marquardt Method for Solving Systems of Nonlinear Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zhenxiang Wu ◽  
Tong Zhou ◽  
Lei Li ◽  
Liang Chen ◽  
Yanfang Ma
Keyword(s):  
Error Bound ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Systems Of Nonlinear Equations ◽  
Local Error ◽  
Local Error Bound ◽  
Marquardt Method ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Local Error Bound Condition

For systems of nonlinear equations, a modified efficient Levenberg–Marquardt method with new LM parameters was developed by Amini et al. (2018). The convergence of the method was proved under the local error bound condition. In order to enhance this method, using nonmonotone technique, we propose a new Levenberg–Marquardt parameter in this paper. The convergence of the new Levenberg–Marquardt method is shown to be at least superlinear, and numerical experiments show that the new Levenberg–Marquardt algorithm can solve systems of nonlinear equations effectively.

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