A convergence analysis of the iteratively regularized Gauss-Newton method under Lipschitz condition
arXiv:0803.237324 citationsh-index: 24
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Provides a theoretical convergence guarantee for a known method under weaker conditions, which is incremental for the field of inverse problems.
The paper proves that the iteratively regularized Gauss-Newton method, under a Lipschitz condition and with an a posteriori stopping rule, is an order optimal regularization method for nonlinear ill-posed inverse problems.
In this paper we consider the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed inverse problems. Under merely Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an order optimal regularization method if the solution is regular in some suitable sense.