10.1007/s40096-023-00515-2

A new adaptive Levenberg–Marquardt parameter with a nonmonotone and trust region strategies for the system of nonlinear equations

  • Zahra Rezaeiparsa1,
  • Ali Ashrafi*1,
  1. Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, IR

Published in Issue 2023-04-25

How to Cite

Rezaeiparsa, Z., & Ashrafi, A. (2023). A new adaptive Levenberg–Marquardt parameter with a nonmonotone and trust region strategies for the system of nonlinear equations. Mathematical Sciences, 18(3 (September 2024). https://doi.org/10.1007/s40096-023-00515-2
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Abstract

Abstract In this paper, we present a modified two-step Levenberg–Marquardt (LM) method with the nonmonotone trust region technique for solving nonlinear equations. In each iteration, not only an LM step is computed, but also an approximate LM step that uses the previously calculated Jacobian. We establish a new adaptive LM parameter and under the local error bound condition the global and cubic convergence of the new method is proved. Numerical results indicate the promising behavior of the suggested algorithm.

Keywords

  • Nonlinear system,
  • Levenberg–Marquardt method,
  • Nonmonotone technique,
  • Trust region method,
  • Cubic convergence

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