A New Modified Efficient Levenberg–Marquardt Method for Solving Systems of Nonlinear Equations
Zhenxiang Wu, Tong Zhou, Lei Li, Liang Chen, Yanfang Ma
Abstract
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.
Topics & Concepts
Levenberg–Marquardt algorithmConvergence (economics)Nonlinear systemApplied mathematicsMathematicsComputer scienceMathematical optimizationAlgorithmArtificial neural networkArtificial intelligencePhysicsEconomicsEconomic growthQuantum mechanicsIterative Methods for Nonlinear EquationsAdvanced Optimization Algorithms ResearchFractional Differential Equations Solutions