Research article

An accelerated adaptive two-step Levenberg–Marquardt method with the modified Metropolis criterion

  • Received: 11 June 2024 Revised: 11 August 2024 Accepted: 15 August 2024 Published: 22 August 2024
  • MSC : 65K05, 90C30

  • In this paper, aiming at the nonlinear equations, a new two-step Levenberg–Marquardt method was proposed. We presented a new Levenberg–Marquardt parameter to obtain the trial step. A new modified Metropolis criterion was used to adjust the upper bound of the approximate step. The convergence of the method was analyzed under the H$ \ddot{\rm o} $lderian local error bound condition and the H$ \ddot\rm o $lderian continuity of the Jacobian. Numerical experiments showed that the new algorithm is effective and competitive in the numbers of functions, Jacobian evaluations and iterations.

    Citation: Dingyu Zhu, Yueting Yang, Mingyuan Cao. An accelerated adaptive two-step Levenberg–Marquardt method with the modified Metropolis criterion[J]. AIMS Mathematics, 2024, 9(9): 24610-24635. doi: 10.3934/math.20241199

    Related Papers:

  • In this paper, aiming at the nonlinear equations, a new two-step Levenberg–Marquardt method was proposed. We presented a new Levenberg–Marquardt parameter to obtain the trial step. A new modified Metropolis criterion was used to adjust the upper bound of the approximate step. The convergence of the method was analyzed under the H$ \ddot{\rm o} $lderian local error bound condition and the H$ \ddot\rm o $lderian continuity of the Jacobian. Numerical experiments showed that the new algorithm is effective and competitive in the numbers of functions, Jacobian evaluations and iterations.



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