A high-order modified Levenberg–Marquardt method for systems of nonlinear equations with fourth-order convergence

Liang Chen

Applied Mathematics and Computation, 2016, vol. 285, issue C, 79-93

Abstract: Fan (2014) presented an accelerated modified Levenberg–Marquardt method for nonlinear equations. At every iteration, the accelerated modified LM method computed not only a LM trial step, but also an additional approximate LM step which employed a line search. In this paper, based on the accelerated modified LM method, we compute the approximate LM step one more time at every iteration, and obtain a high-order accelerating modified Levenberg–Marquardt method. Under the local error bound condition which is weaker than nonsingularity, the convergence order of this new method is shown to be fourth. A globally convergence is also given by the trust region technique. Numerical results show that the new method is efficient and could save many calculations of the Jacobian.

Keywords: Unconstrained optimization; Trust region; Systems of nonlinear equations; Levenberg–Marquardt method; Local error bound (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:285:y:2016:i:c:p:79-93

DOI: 10.1016/j.amc.2016.03.031

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