Date: Wednesday December 7th 2022

Time: 11:00am to noon

Speaker: Miroslav Rozložník

Affiliation: Institute of Mathematics of the Academy of Sciences of the Czech Republic

Title: Iterated Gauss-Seidel GMRES
Mode: Hybrid. Speaker will be in-person. Attendance can be in-person or remote.

Remote Attendance: contact mathstats-staff@ucdenver.edu for Zoom information

In-person Attendance: Student Commons Building, room 4113

Abstract: 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.