Iterated Gauss-Seidel Gram - Schmidt process - Events

Iterated Gauss-Seidel Gram - Schmidt process

Date: 24. 11. 2022
Time: 14:00 - 15:30
Address:
Sokolovská 83, Praha
Room: K3
Speaker: Miroslav Rozložník

We present an iterated Gauss-Seidel formulation of the GMRES algorithm (IGS-GMRES) based on the ideas of Ruhe (1983) and Swirydowicz et al. (2020). IGS-GMRES maintains orthogonality to the level O(eps) kappa(B) or O(eps), depending on the choice of one or two iterations; for two Gauss-Seidel iterations, the computed Krylov basis vectors remain orthogonal to working accuracy. The resulting GMRES method is thus backward stable. We show that IGS-GMRES can be implemented with only a single synchronization point per iteration, making it relevant to large-scale parallel computing environments.