Agah D. Garnadi
A LEPSKIJ-TYPE STOPPING-RULE FOR SIMPLIFIED ITERATIVELY REGULARIZED GAUSS-NEWTON METHOD
(250K, pdf)

ABSTRACT.  Iterative regularization methods for nonlinear ill-posed equations of the form $ F(a)= y$, where $ F: D(F) \subset X 	o Y$ is an operator between Hilbert spaces $ X $ and $ Y$, usually involve calculation of the Fr\'{e}chet derivatives of $ F$ at each iterate and at the unknown solution $ a^\sharp$. A modified form of the generalized Gauss-Newton method which requires the Fr\'{e}chet derivative of $F$ only at an initial approximation $ a_0$ of the solution $ a^\sharp$ as studied by Mahale and Nair. This work studied an {\it a posteriori} stopping rule of Lepskij-type of the method. A numerical experiment 
from inverse source potential problem is demonstrated.