Accuracy Estimation for a Class of Iteratively Regularized Gauss–Newton Methods with a posteriori Stopping Rule

AbstractA class of iteratively regularized Gauss–Newton methods for solving irregular nonlinear equations with smooth operators in a Hilbert space is investigated. The iteration stopping rule is an a posteriori one similar to V.A. Morozov’s discrepancy principle. The regularizing property of the iterations is established, and an accuracy estimate for the resulting approximation is obtained assuming that the sought solution satisfies the source condition. The estimate is given in terms of the error of the operator without imposing any structural conditions on this operator.