An efficient m-step Levenberg-Marquardt method for nonlinear equations

分类： 数学 >> 控制和优化 分类： 数学 >> 计算数学 提交时间： 2016-07-11

Chen, Liang Ma, Yanfang Su, Chencheng

摘要： In this paper, we construct and analyze an efficient m-step Levenberg-Marquardt method for nonlinear equations. The main advantage of this method is that the m-step LM method could save more Jacobian calculations with frozen $(J_k^TJ_k+\lambda_kI)^{-1}J_k^T$ at every iteration. Under the local error bound condition which is weaker than nonsingularity, the m-step LM method has been proved to have $(m+1)$th convergence order. The global convergence has also been given by trust region technique. Numerical results show that the m-step LM method is efficient and could save many calculations of the Jacobian especially for large scale problems.

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