On Tue, Aug 3, 2010 at 10:54 PM, Filippo Spiga < filippo.spiga at disco.unimib.it> wrote:
> Dear Hong, > >> This confirms that your Jacobian is singular, thus none of linear >> solvers would work. >> > > So do any preconditioner not help me to solve the problem? > There can exist no solutions when the matrix is singular, thus you have a problem with either: a) the problem definition b) the creation of your matrix in PETSc > I put some stuff here: http://tinyurl.com/fil-petsc > - "A_LS.m" is matrix (saved by PETSc) > - "b_LS-m" > - the file "eigenvalues_A" contains the eigenvalues of the matrix A, > computed by MATLAB. > > I used "-pc_type lu" and 1 only processor. The result is the same of my > previous email (*). > This shows that your matrix is singular. > Anyway if I solve the problem using MATLAB I get the right solution. The > formulation seems correct. To be What does this mean? What method in MATLAB? Some methods (like CG) can iterate on rank deficient matrices with a compatible rhs and get a solution, but other Krylov methods will fail. Most preconditioners will fail. > honest, the eigenvalues don't say me nothing. But I'm a computer scientist, > not a mathematician. I'm not able to recognize which preconditioner I should > use or which modifications (scaling all/part of the rows? reformulate the > system in another way?...) do to solve the problem. From my side, it is not > possible to try all the preconditioners and also it is not the right way... > Actually, I strongly disagree. Preconditioners are very problem specific, and it is often impossible to prove which one will work for a certain problem. There are many well-known results along these lines, such as the paper of Greenbaum, Strakos, and Ptak on GMRES. Experimentation is essential. Matt > Once again, thanks. > > (*) > [0|23:14:58]: unknown: MatLUFactorNumeric_SeqAIJ() line 668 in > src/mat/impls/aij/seq/aijfact.c: Zero pivot row 1 value 0 tolerance > 2.77778e-14 * rowsum 0.0277778 > > -- > > Filippo SPIGA > > ?Nobody will drive us out of Cantor's paradise.? > -- David Hilbert > > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20100803/500d0d0e/attachment.htm>
