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- Title
An efficient m-step Levenberg-Marquardt method for systems of nonlinear equations.
- Authors
Liang Chen; Yanfang Ma
- Abstract
In this paper, we propose an efficient m-step Levenberg-Marquardt method for systems of nonlinear equations. At every iteration, the efficient m-step LM method computes not only the classical LM step, but also m-1 approximate LM steps with frozen (JTk Jk+λkI)-1JTk. Also, we employ m-1 line searches for m-1 approximate LM steps for better numerical performance. Under the local error bound condition which is weaker than nonsingularity, the efficient m-step LM method has been proved to have (m+1)th convergence order. The global convergence has also been given by trust region technique. Numerical results show that the efficient m-step LM method is efficient and could save many calculations of the Jacobian especially for large scale problems.
- Subjects
NONLINEAR equations; APPROXIMATION theory; STOCHASTIC convergence; MATHEMATICAL proofs; JACOBIAN matrices
- Publication
Journal of Computational Analysis & Applications, 2020, Vol 28, Issue 3, p543
- ISSN
1521-1398
- Publication type
Article