The Cimmino Algorithm in a Hilbert Space

In this chapter we study the convergence of the Cimmino algorithm for solving star-shaped feasibility problems in a Hilbert space. Our main goal is to obtain an approximate solution of the problem in the presence of computational errors. We show that the Cimmino algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant. Moreover, for a known computational error, we find out what an approximate solution can be obtained and how many iterates one needs for this.