TY - JOUR
T1 - On a class of frozen regularized Gauss-Newton methods for nonlinear inverse problems
AU - Jin, Qinian
PY - 2010
Y1 - 2010
N2 - In this paper we consider a class of regularized Gauss-Newton methods for solving nonlinear inverse problems for which an a posteriori stopping rule is proposed to terminate the iteration. Such methods have the frozen feature that they require only the computation of the Fŕechet derivative at the initial approximation. Thus the computational work is considerably reduced. Under certain mild conditions, we give the convergence analysis and derive various estimates, including the order optimality, on these methods.
AB - In this paper we consider a class of regularized Gauss-Newton methods for solving nonlinear inverse problems for which an a posteriori stopping rule is proposed to terminate the iteration. Such methods have the frozen feature that they require only the computation of the Fŕechet derivative at the initial approximation. Thus the computational work is considerably reduced. Under certain mild conditions, we give the convergence analysis and derive various estimates, including the order optimality, on these methods.
KW - A posteriori stopping rule
KW - Convergence
KW - Frozen regularized Gauss-Newton method
KW - Nonlinear inverse problems
KW - Order optimality
UR - http://www.scopus.com/inward/record.url?scp=77956577037&partnerID=8YFLogxK
U2 - 10.1090/S0025-5718-10-02359-8
DO - 10.1090/S0025-5718-10-02359-8
M3 - Article
SN - 0025-5718
VL - 79
SP - 2191
EP - 2211
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 272
ER -