[petsc-users] Slepc: B not semi-positive definite

[Jose E. Roman]

El 04/08/2014, a las 16:17, Andrea Fani escribió:

> Hello,
> 
> I have to solve a  generalized eigenvalue problem Ax=sigma B x.
> 
> A is not hermitian. B is singular and is slightly not hermitian (only few elements breaks the symmetry). 
> 
> I used the standard  krilov-shur algorithm with a shift and invert tranformation and it seems to work fine, but I am a bit worried since in the documentation it is treated only the case with B singular but symmetric.
> 
> Andrea

Symmetric Krylov methods in SLEPc use the B-inner product, so if B is singular we need to do purification of the computed solution to remove directions in the nullspace of B. Non-symmetric Krylov solvers use the standard inner product (not the B-inner product), so purification is not necessary.

Jose