[petsc-users] Is there efficeint method for matrix with one extremely small eigen value?

[Umut Tabak]

On 04/06/2011 04:50 PM, Jed Brown wrote:
> On Wed, 06 Apr 2011 16:37:26 +0200, Umut Tabak <u.tabak at tudelft.nl> 
> wrote:
>> Just curious, are not the other negative eigenvalues problematic as 
>> well?
>
> Negative eigenvalues do not pose any particular problem to Krylov 
> methods like GMRES. Conjugate gradients does require that the matrix 
> be SPD, but petsc-dev detects when a matrix is negative definite and 
> still does the right thing. 

Also with cg type methods? if yes, how?

Because I am dealing with a similar problem in a projection sense which 
makes some factors that are already available very good preconditioners, 
completely problem specific, then cg converges incredibly fast, sth like 
4 to 8 iterations. However, projection is the key and at every step, in 
cg, I should make sure that the search directions in cg are orthogonal 
to the previous ones by cgs/mgs, otherwise I bump into the well know 
orthogonality issues of Lanczos type methods...

why I am digging is to see some better options if there are any.

Greetz,
Umut