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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.

Details

Date:
February 16, 2022
Time:
10:30 - 11:30 CST
Event Category:

Venue

https://wordpress.cels.anl.gov/cels-seminars/event/lans-seminar-35/