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

[Jed Brown]

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. With petsc-3.1, you could simply change the sign of everything. (I prefer to build to formulate my equations with positive matrices when possible, but those other negative eigenvalues are not the problem here.)