TY - JOUR
T1 - A note on the Levenberg-Marquardt parameter
AU - Fan, Jinyan
AU - Pan, Jianyu
PY - 2009/1/15
Y1 - 2009/1/15
N2 - 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 kth iteration is chosen as λk = θ {norm of matrix} Fk {norm of matrix}2 + (1 - θ) {norm of matrix} JkT Fk {norm of matrix}2 where F is the residual function, J is the Jacobi of F, and θ ∈ [0, 1] is a constant. In this note, we point out that the LM parameter can be any combination of {norm of matrix} Fk {norm of matrix}2 and {norm of matrix} JkT Fk {norm of matrix}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. Crown
AB - 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 kth iteration is chosen as λk = θ {norm of matrix} Fk {norm of matrix}2 + (1 - θ) {norm of matrix} JkT Fk {norm of matrix}2 where F is the residual function, J is the Jacobi of F, and θ ∈ [0, 1] is a constant. In this note, we point out that the LM parameter can be any combination of {norm of matrix} Fk {norm of matrix}2 and {norm of matrix} JkT Fk {norm of matrix}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. Crown
KW - Levenberg-Marquardt method
KW - Nonlinear equations
KW - Quadratic convergence
UR - https://www.scopus.com/pages/publications/58349084113
U2 - 10.1016/j.amc.2008.10.056
DO - 10.1016/j.amc.2008.10.056
M3 - 文章
AN - SCOPUS:58349084113
SN - 0096-3003
VL - 207
SP - 351
EP - 359
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 2
ER -