TY - JOUR
T1 - Inexact Levenberg-Marquardt method for nonlinear equations
AU - Fan, Jinyan
AU - Pan, Jianyu
PY - 2004/11
Y1 - 2004/11
N2 - In this paper, we present an inexact Levenberg-Marquardt (LM) method for singular system of nonlinear equations, where the LM parameter is chosen as the norm of the function and the trial step is computed approximately. Under the local error bound condition which is weaker than the nonsingularity, we show that the new inexact LM method preserves the quadratic convergence of the traditional LM method where the parameter is chosen to be larger than a positive constant and the Jacobi at the solution is nonsingular.
AB - In this paper, we present an inexact Levenberg-Marquardt (LM) method for singular system of nonlinear equations, where the LM parameter is chosen as the norm of the function and the trial step is computed approximately. Under the local error bound condition which is weaker than the nonsingularity, we show that the new inexact LM method preserves the quadratic convergence of the traditional LM method where the parameter is chosen to be larger than a positive constant and the Jacobi at the solution is nonsingular.
KW - Levenberg-Marquardt method
KW - Local error bound condition
KW - Nonlinear equations
KW - Quadratic convergence
UR - https://www.scopus.com/pages/publications/4944258487
U2 - 10.3934/dcdsb.2004.4.1223
DO - 10.3934/dcdsb.2004.4.1223
M3 - 文章
AN - SCOPUS:4944258487
SN - 1531-3492
VL - 4
SP - 1223
EP - 1232
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 4
ER -