Abstract

In this article we investigate and prove relationships between metric and Bregman projections induced by powers of the norm of a Banach space. We consider Bregman projections onto affine subspaces of Banach spaces and deduce some interesting analogies to results which are well known for Hilbert spaces. Using these concepts as well as ideas from sequential subspace optimization techniques we construct efficient iterative methods to compute Bregman projections onto affine subspaces that are connected to linear, bounded operators between Banach spaces. Especially these methods can be used to compute minimum-norm solutions of linear operator equations or best approximations in the range of a linear operator. Numerical experiments illuminate the performance of our iterative algorithms and demonstrate a significant acceleration compared to the Landweber method.