TY - JOUR
T1 - On a heuristic stopping rule for the regularization of inverse problems by the augmented Lagrangian method
AU - Jin, Qinian
N1 - Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
PY - 2017/8/1
Y1 - 2017/8/1
N2 - In this paper we propose a heuristic stopping rule of Hanke–Raus type for the regularization of linear ill-posed inverse problems by the augmented Lagrangian method. This stopping rule requires no information on the noise level. Under certain source conditions, we derive a posteriori error estimates in term of Bregman distance. By imposing certain conditions on the noise data, we establish convergence results. Numerical results are presented to illustrate the performance.
AB - In this paper we propose a heuristic stopping rule of Hanke–Raus type for the regularization of linear ill-posed inverse problems by the augmented Lagrangian method. This stopping rule requires no information on the noise level. Under certain source conditions, we derive a posteriori error estimates in term of Bregman distance. By imposing certain conditions on the noise data, we establish convergence results. Numerical results are presented to illustrate the performance.
KW - 47H17
KW - 65J15
KW - 65J20
UR - http://www.scopus.com/inward/record.url?scp=85007492365&partnerID=8YFLogxK
U2 - 10.1007/s00211-016-0860-8
DO - 10.1007/s00211-016-0860-8
M3 - Article
SN - 0029-599X
VL - 136
SP - 973
EP - 992
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 4
ER -