REFERENCES

There is a class of linear problems for which a matrix-vector product is very time consuming to compute since an expensive approximation method is necessary to compute it with some prescribed relative precision. One important example is simulations in lattice QCD with Neuberger fermions where a matrix multiply requires the product of the matrix sign function of a large sparse matrix times a vector. For this, a Lanczos type of method can be used [6, 1, 5]. Other examples arise from Schur complement systems where a coupled system of linear equations is solved by eliminating one part of the variables. The resulting linear system can be solved by straightforwardly applying an iterative method in which in every step, for the matrix-vector product, a linear system must be solved to a certain precision [3, 9]. The recent interest in these type of applications has resulted in research efforts to study the effect of errors in the matrix-vector products on iterative linear system solvers [2, 7, 4]. Some iterative system solvers turn out to be more sensitive than others [8]. For various Krylov subspace methods, so-called, relaxation strategie