The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence

@article{Fan2012TheML,
  title={The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence},
  author={Jinyan Fan},
  journal={Math. Comput.},
  year={2012},
  volume={81},
  pages={447-466}
}
  • Jinyan Fan
  • Published 2012
  • Computer Science, Mathematics
  • Math. Comput.
We propose a modified Levenberg-Marquardt method for nonlinear equations, in which not only a LM step but also an approximate LM step are computed at every iteration. To ensure the global convergence of the new method, a new kind of predicted reduction is introduced for the merit function when using the trust region technique. The cubic convergence of the modified LM method is proved under the local error bound condition which is weaker than nonsingularity. Numerical results show that the new… Expand
60 Citations
A modified Levenberg–Marquardt method with line search for nonlinear equations
  • L. Chen
  • Mathematics, Computer Science
  • Comput. Optim. Appl.
  • 2016
  • 5
A higher-order Levenberg-Marquardt method for nonlinear equations
  • X. Yang
  • Mathematics, Computer Science
  • Appl. Math. Comput.
  • 2013
  • 23
A high-order modified Levenberg-Marquardt method for systems of nonlinear equations with fourth-order convergence
  • L. Chen
  • Mathematics, Computer Science
  • Appl. Math. Comput.
  • 2016
  • 11
  • Highly Influenced
A corrected Levenberg-Marquardt algorithm with a nonmonotone line search for the system of nonlinear equations
  • 7
On a New Updating Rule of the Levenberg–Marquardt Parameter
  • 1
A modified two steps Levenberg-Marquardt method for nonlinear equations
  • 29
An Adaptive Multi-step Levenberg–Marquardt Method
  • 2
A Shamanskii-like Levenberg-Marquardt method for nonlinear equations
  • Jinyan Fan
  • Mathematics, Computer Science
  • Comput. Optim. Appl.
  • 2013
  • 7
Three-steps modified Levenberg-Marquardt method with a new line search for systems of nonlinear equations
  • 14
  • Highly Influenced
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 24 REFERENCES
A MODIFIED LEVENBERG-MARQUARDT ALGORITHM FOR SINGULAR SYSTEM OF NONLINEAR EQUATIONS
  • 66
  • Highly Influential
On the Rate of Convergence of the Levenberg-Marquardt Method
  • 293
  • Highly Influential
On the Quadratic Convergence of the Levenberg-Marquardt Method without Nonsingularity Assumption
  • 178
  • PDF
Tensor Methods for Nonlinear Equations.
  • 129
A note on the Levenberg-Marquardt parameter
  • 43
A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES
  • 9,402
  • PDF
Trust Region Algorithms for Nonlinear Equations
  • 33
Recent Developments in Algorithms and Software for Trust Region Methods
  • 379
Iterative methods for optimization
  • C. Kelley
  • Mathematics, Computer Science
  • Frontiers in applied mathematics
  • 1999
  • 1,744
  • PDF
...
1
2
3
...