Abstract Preconditioned Krylov subspace solvers are an important and frequently used technique for solving large sparse linear systems. There are many advantageous properties concerning convergence rates and error estimates. However, implementing such a solver on a computer, we often observe an unexpected and even contrary behavior. The purpose of this paper is to show that this gap between the theoretical and practical behavior can be narrowed by using a problem-oriented arithmetic. In addition we give rigorous error bounds to our computed results.