[petsc-users] minres and gmres difference

[Barry Smith]

 Also what happens when you crank the restart of GMRES to above 155? I bet it converges. I am not implying that this would be practical but it would tell you something, there is no theory for GMRES with restart.

   Barry

On Mar 1, 2011, at 2:45 PM, Umut Tabak wrote:

> Dear list,
> 
> While testing an ill-conditioned system solution with minres and gmres(default 30 restarts, and no other options) in PETSc, I came up with the result that the system is solved in 155 iterations by minres to a relative default tolerance but it could not be solved by gmres.
> 
> The original system is indefinite and had a condition number on the order of 10e+6, with a diagonal conditioning left and right, I could lower the condition number to the order of 10e+4 (however still indefinite with negative eigenvalues) and try to solve this system. On the other hand, I am also trying to understand the details of minres and gmres, so they both minimize the 2 norm of residual by solving a least squares problem where the latter is for unsymmetric systems, and the other is using a 3-term recurrence relation similar to cg (which I am trying to figure out now.). I would expect both to give the same result in PETSc however gmres fails. I wanted to check also gmres because I read in
> 
> "Iterative Krylov Methods for Large Linear Systems" van der Vorst, Chap.6 Gmres and Minres, page 86
> 
> where it is mentioned that gmres could be more robust and less vulnerable to rounding errors than minres.
> 
> What could be the reason for this? Any comments are appreciated
> 
> Best,
> Umut