The authors investigate iterative regularization methods for solving linear and nonlinear systems of ill-posed operator equations in Hilbert space. The basic idea consists in incorporating a bang-bang relaxation parameter in the classical Landweber-Kaczmarz approach of regularization, combined with a new stopping rule. The new method is called loping Landweber-Kaczmarz method.
Another regularization strategy considered in this article is an embedding approach. The convergence analysis of the iterative regularization loping Landweber-Kaczmarz method is developed under standard assumptions. Then the algorithm of the embedded Landweber-Kaczmarz method is described and convergence and stability results are proved.
One advantage of this type of methods is the fact that the resulting regularizing methods better explore the special structure of the model and the pointwise noise-estimate. As the authors show, the new methods of regularization allow fast implementation.