Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4633740 | Applied Mathematics and Computation | 2009 | 9 Pages |
Abstract
In [C. Ma, L. Jiang, Some research on Levenberg–Marquardt method for the nonlinear equations, Appl. Math. Comput. 184 (2007) 1032–1040], the LM parameter at the k th iteration is chosen as λk=θ‖Fk‖2+(1-θ)‖JkTFk‖2 where F is the residual function, J is the Jacobi of F , and θ∈[0,1]θ∈[0,1] is a constant. In this note, we point out that the LM parameter can be any combination of ‖Fk‖2‖Fk‖2 and ‖JkTFk‖2 provided it is positive. Furthermore, we give a more general choice of the LM parameter, and show that the LM method still preserves the quadratic convergence under the local error condition which is weaker than nonsingularity.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Jinyan Fan, Jianyu Pan,