[petsc-dev] GMRES and eigen estimates

[Barry Smith]

barry-smiths-macbook-pro:tutorials barrysmith$ ./ex10 -f0 ~/Datafiles/Matrices/arco1 -pc_type lu -ksp_type gmres -ksp_monitor_singular_value
  0 KSP Residual norm 2.544968574075e+03 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
  1 KSP Residual norm 2.708628636814e-10 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
Number of iterations =   1
Residual norm 2.36559e-11
barry-smiths-macbook-pro:tutorials barrysmith$ ./ex10 -f0 ~/Datafiles/Matrices/arco1 -pc_type lu -ksp_type fgmres -ksp_monitor_singular_value
  0 KSP Residual norm 7.410897708964e+00 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
  1 KSP Residual norm 2.157675690523e-11 % max 9.999999999999e-01 min 9.999999999999e-01 max/min 1.000000000000e+00
Number of iterations =   1
Residual norm 2.26094e-11
barry-smiths-macbook-pro:tutorials barrysmith$ ./ex10 -f0 ~/Datafiles/Matrices/arco1 -pc_type lu -ksp_type cg -ksp_monitor_singular_value
  0 KSP Residual norm 2.544968574075e+03 % max 1.000000000000e+00 min 1.000000000000e+00 max/min 1.000000000000e+00
  1 KSP Residual norm 3.135993325987e-10 % max 9.999999999999e-01 min 9.999999999999e-01 max/min 1.000000000000e+00
Number of iterations =   1
Residual norm 2.22684e-11

  Mark,

   Could you provide the exact specifications on how you obtained this bad highest eigen estimate? What code you ran with what options?

    Thanks

    barry


On Mar 30, 2012, at 10:22 AM, Mark F. Adams wrote:

> I've had problems with GMRES and eigen estimates in the past but I now have a smoking gun.  It seems that if you give GMRES an operator preconditioned with LU (ie, the preconditioned operator is the identity) GMRES gives me a highest eigen estimate of ~10 (way off).  With CG I get a prefect max=1.0, min=0.0.
> 
> Any thoughts?
> 
> Mark