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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran

    Zahra Rezaeiparsa & Ali Ashrafi

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  1. Zahra Rezaeiparsa
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  2. Ali Ashrafi
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Correspondence to Ali Ashrafi.

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Rezaeiparsa, Z., Ashrafi, A. A new adaptive Levenberg–Marquardt parameter with a nonmonotone and trust region strategies for the system of nonlinear equations. Math Sci (2023). https://doi.org/10.1007/s40096-023-00515-2

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