Variable Accuracy of Matrix-Vector Products in Projection Methods for Eigencomputation
- Valeria Simoncini
- SIAM J. Numerical Analysis
There are classes of linear problems for which a matrix-vector product is a time consuming operation because an expensive approximation method is required to compute it to a given accuracy. 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. The recent interest in this and similar type of applications has resulted in research efforts to study the effect of errors in the matrix-vector products on iterative linear system solvers. In this paper we give a very general and abstract discussion on this issue and try to provide insight into why some iterative system solvers are more sensitive than others.