Article ID Journal Published Year Pages File Type
4633740 Applied Mathematics and Computation 2009 9 Pages PDF
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
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