Iteratively regularized Gauss–Newton method for operator equations with normally solvable derivative at the solution

We study the iteratively regularized Gauss–Newton method in a Hilbert space for solving irregular nonlinear equations with smooth operators having normally solvable derivatives at the solution. We consider both a priori and a posteriori stopping criterions for the iterations and establish accuracy estimates for resulting approximations. In the case where the a priori stopping rule is used, the accuracy of approximations arises to be proportional to the error level in input data. The latter result generalizes well-known estimates of this kind obtained for linear equations with normally solvable operators.