Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing 论文

摘要

We provide a general framework for the understanding of Inexact Krylov subspace methods for the solution of symmetric and nonsymmetric linear systems of equations, as well as for certain eigenvalue calculations. This framework allows us to explain the empirical results reported in a series of CERFACS technical reports by Bouras, Fraysse and Giraud in 2000. Furthermore, assuming exact arithmetic, our analysis produces computable criteria to bound the inexactness of the matrix{vector multiplication in such a way as to maintain the convergence of the Krylov subspace method. The theory developed is applied to several problems including the solution of Schur complement systems, linear systems which depend on a parameter, and eigenvalue problems. Numerical experiments for some of these scienti c applications are reported, where the computable criteria are successfully applied.