- This event has passed.
LANS Seminar
February 16, 2022 @ 10:30 - 11:30 CST
Seminar Title: GPMR: An Iterative Method for Square Partitioned Linear Systems
Speaker: Alexis Montoison
Title: PhD Student
Affiliation: Polytechnique Montreal
Date/Time: February 16, 2022 / 10:30 AM – 11:30 AM
Location: See meeting URL on the cels-seminars website (requires Argonne login)
Host: Francois Pacaud
Description: We present a new iterative method named GPMR (General Partitioned Minimal Residual) for square 2×2 block linear systems. GPMR is based on a new process that simultaneously reduces two rectangular matrices to upper Hessenberg form and is closely related to the block-Arnoldi process. We compare the performance of GPMR with GMRES on linear systems from the SuiteSparse Matrix Collection. In our experiments, GPMR terminates significantly earlier than GMRES on a residual-based stopping condition with an improvement ranging from around 10% up to 50% in terms of number of iterations.
GPMR is implemented in Julia, as part of our Krylov.jl collection of Krylov methods. Krylov.jl provides Julia implementations of a growing number of the most useful Krylov method for linear systems, least-squares, and least-norm problems, together with facilities for saddle-point systems. We illustrate the main features of Krylov.jl on our implementation of GPMR.
Please note that the meeting URL for this event can be seen on the cels-seminars website, which requires an Argonne login.