Solving for (approximate) convex feasibility under finite precision

Abstract

In the present paper we study convergence of projection algorithms for solving convex fea- sibility problems in a Hilbert space. Our goal is to obtain an ε-approximate solution of the problem in the presence of computational errors, where ε is a given positive number.We show that our projection algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant.