Abstract
Krylov subspace recycling is a well-known technique for reusing information across sequential invocations of a Krylov subspace method on systems with the same or a slowly changing coefficient matrix. In this talk, we present a mixed precision GMRES-based iterative refinement solver incorporated with Krylov subspace recycling approach.
The insight in this algorithm is that in each refinement step, we call preconditioned GMRES on a linear system with the same coefficient matrix, with only the right-hand side changing. In this way, the GMRES solves in subsequent refinement steps can be accelerated by recycling information obtained from the first step.
After giving a background on GMRES-based iterative refinement and Krylov subspace recycling, we present numerical experiments that show the advantage of combining this approach.