## What's the role of restart in PGMRES?

Open discussion for MAGMA library (Matrix Algebra on GPU and Multicore Architectures)
hsahasra
Posts: 32
Joined: Mon Jun 24, 2013 3:40 pm

### What's the role of restart in PGMRES?

Hi,

I have been experimenting solving a linear system with PGMRES+Jacobi preconditioner. The solver diverges with default restart. When I set the restart at 400, it converges in ~700 iterations. The number of iterations increases if I increase or decrease the restart from 400. How should I decide what restart is needed? Does the restart parameter change from system to system?

Quantity in brackets after PGMRES is the restart value. E.g. PGMRES(30) is with restart=30.

%=============================================================%
% PGMRES(30) solver summary:
% initial residual: 2.000000e+02
% iterations: 1000
% exact final residual: 4.569463e+00
% runtime: 1.0274 sec
%=============================================================%

%=============================================================%
% PGMRES(100) solver summary:
% initial residual: 2.000000e+02
% iterations: 1000
% exact final residual: 9.811325e-03
% runtime: 2.7982 sec
%=============================================================%

%=============================================================%
% PGMRES(400) solver summary:
% initial residual: 2.000000e+02
% iterations: 697
% exact final residual: 1.183331e-09
% runtime: 6.5171 sec
%=============================================================%

%=============================================================%
% PGMRES(500) solver summary:
% initial residual: 2.000000e+02
% iterations: 761
% exact final residual: 1.037513e-09
% runtime: 8.2672 sec
%=============================================================%

%=============================================================%
% PGMRES(350) solver summary:
% initial residual: 2.000000e+02
% iterations: 871
% exact final residual: 8.002018e-10
% runtime: 7.2320 sec
%=============================================================%

Thanks,

hartwig anzt
Posts: 90
Joined: Tue Sep 02, 2014 5:44 pm