[petsc-users] [SLEPc] Krylov-Schur convergence

[Jose E. Roman]

This is really strange. We cannot say what is going on, everything seems fine.
Could you try solving the problem as non-Hermitian to see what happens? Just run with -eps_non_hermitian. Depending on the result, we can suggest other things to try.
Jose


> El 13 nov 2018, a las 10:58, Ale Foggia via petsc-users <petsc-users at mcs.anl.gov> escribió:
> 
> Hello,
> 
> I'm using SLEPc to get the smallest real eigenvalue (EPS_SMALLEST_REAL) of a Hermitian problem (EPS_HEP). The linear size of the matrices I'm solving is around 10**9 elements and they are sparse. I've asked a few questions before regarding the same problem setting and you suggested me to use Krylov-Schur (because I was using Lanczos). I tried KS and up to a certain matrix size the convergence (relative to the eigenvalue) is good, it's around 10**-9, like with Lanczos, but when I increase the size I start getting the eigenvalue with only 3 correct digits. I've used the options: -eps_tol 1e-9 -eps_mpd 100 (16 was the default), but the only thing I got is one more eigenvalue with the same big error, and the iterations performed were only 2. Why didn't it do more in order to reach the convergence? Should I set other parameters? I don't know how to work out this problem, can you help me with this please? I send the -eps_view output and the eigenvalues with its errors:
> 
> EPS Object: 2048 MPI processes
>   type: krylovschur
>     50% of basis vectors kept after restart
>     using the locking variant
>   problem type: symmetric eigenvalue problem
>   selected portion of the spectrum: smallest real parts
>   number of eigenvalues (nev): 1
>   number of column vectors (ncv): 101
>   maximum dimension of projected problem (mpd): 100
>   maximum number of iterations: 46210024
>   tolerance: 1e-09
>   convergence test: relative to the eigenvalue
> BV Object: 2048 MPI processes
>   type: svec
>   102 columns of global length 2333606220
>   vector orthogonalization method: classical Gram-Schmidt
>   orthogonalization refinement: if needed (eta: 0.7071)
>   block orthogonalization method: GS
>   doing matmult as a single matrix-matrix product
> DS Object: 2048 MPI processes
>   type: hep
>   parallel operation mode: REDUNDANT
>   solving the problem with: Implicit QR method (_steqr)
> ST Object: 2048 MPI processes
>   type: shift
>   shift: 0.
>   number of matrices: 1
> 
>               k                ||Ax-kx||/||kx||
>    -----------------        ------------------
>      -15.093051         0.00323917 (with KS)
>      -15.087320         0.00265215 (with KS)
>      -15.048025         8.67204e-09 (with Lanczos)
> Iterations performed 2
> 
> Ale