A Polynomial Rate of Asymptotic Regularity for Compositions of Projections in Hilbert Space

This paper provides an explicit polynomial rate of asymptotic regularity for (in general inconsistent) feasibility problems in hilbert space. in particular, we give a quantitative version of bauschke’s solution of the zero displacement problem as well as of various generalizations of this problem. the results in this paper have been obtained by applying a general proof-theoretic method for the extraction of effective bounds from proofs due to the author (‘proof mining’) to bauschke’s proof.