2 research outputs found
GMRES convergence bounds for eigenvalue problems
The convergence of GMRES for solving linear systems can be influenced heavily
by the structure of the right hand side. Within the solution of eigenvalue
problems via inverse iteration or subspace iteration, the right hand side is
generally related to an approximate invariant subspace of the linear system. We
give detailed and new bounds on (block) GMRES that take the special behavior of
the right hand side into account and explain the initial sharp decrease of the
GMRES residual. The bounds give rise to adapted preconditioners applied to the
eigenvalue problems, e.g. tuned and polynomial preconditioners. The numerical
results show that the new (block) GMRES bounds are much sharper than
conventional bounds and that preconditioned subspace iteration with either a
tuned or polynomial preconditioner should be used in practice.Comment: second revised versio