Thanks! Does the purify option only changes the eigenvector without influencing the eigenvalue?
-Manav > On Dec 5, 2019, at 1:54 AM, Jose E. Roman <[email protected]> wrote: > > In symmetric problems (GHEP) you might have large residuals due to B being > singular. The explanation is the following. By default, in SLEPc GHEPs are > solved via a B-Lanczos recurrence, that is, using the inner product induced > by B. If B is singular this is not a true inner product and numerical > problems may arise, in particular, the computed eigenvectors may be corrupted > with components in the null space of B. This is easily solved by a small > computation called 'eigenvector purification' which is on by default in > SLEPc, see EPSSetPurify(). This is described with a bit more detail in > section 3.4.4 of the manual. > > In non-symmetric problems (GNHEP) you should not see this problem. The only > precaution is not to solve systems with matrix B, e.g., using > shift-and-invert. > > Jose > > >> El 5 dic 2019, a las 5:04, Manav Bhatia <[email protected]> escribió: >> >> Hi, >> >> I am working on mixed form finite element discretization which leads to >> eigenvalues of the form >> >> A x = lambda B x >> >> With the matrices defined in a block structure as >> >> A = [ K D^T ] >> [ D 0 ] >> >> B = [ M 0 ] >> [ 0 0 ] >> >> The second row of equations come from Lagrange multipliers in our >> discretization scheme. A system with m Lagrange multiplier is expected to >> have m Inf eigenvalues. We are testing the standard eigensolvers in Matlab >> and as the system size increases the eigensolves are stopping with larger >> residuals, || r_i ||, of the eigensystem: >> >> r_i = A x_i - lambda_i B x_i >> >> I am working towards setting this up in SLEPc. In the meantime I am curious >> about the following: >> >> 1. Is the eigensolution of such systems known to be problematic? >> 2. Are there standard tricks in SLEPc or elsewhere that are geared towards >> more robust solutions of such systems? >> >> I would appreciate guidance on this. >> >> Regards, >> Manav >> >> >
