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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. 

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