Brakhage's Implicit Iteration Method and the Information Complexity of Equations with Operators Having Closed Range

Abstract An a posteriori stopping rule connected with monitoring the norm of the second residual is introduced for Brakhage's implicit nonstationary iteration method, applied to ill-posed problems involving linear operators with closed range. It is also shown that for some classes of equations with such operators, the algorithm consisting in combination of Brakhage's method with some new discretization scheme is order optimal in the sense of information-based complexity.