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A New Modified Levenberg–Marquardt Method for Systems of Nonlinear Equations

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  • Liang Chen
  • Yanfang Ma
  • Guotao Wang

Abstract

Taking a new choice of the LM parameter λk=μkJkTFkδ with δ∈0,2, we give a new modified Levenberg–Marquardt method. Under the error bound condition c distw,S≤JwTFw which is weaker than the nonsingular of Jacobian Jw, we present that the new Levenberg–Marquardt method has at least superlinear convergence when δ∈0,1 and quadratic convergence when δ∈1,2, respectively, which indicates that our new Levenberg–Marquardt method is performed for the systems of nonlinear equations. Also, numerical experiments indicate its efficiency on a set of systems of nonlinear equations.

Suggested Citation

  • Liang Chen & Yanfang Ma & Guotao Wang, 2023. "A New Modified Levenberg–Marquardt Method for Systems of Nonlinear Equations," Journal of Mathematics, Hindawi, vol. 2023, pages 1-13, February.
    • Handle: RePEc:hin:jjmath:6043780
    DOI: 10.1155/2023/6043780
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