# [Trilinos-Users] Strange eigen vectors in Anasazi -- follow up

Chris Baker cgbaker at gmail.com
Sun Mar 9 09:06:27 MDT 2008

```Davood,

You are correct. The eigenvectors are only unique for distinct eigenvalues.
For the case that A == identity == B, LOBPCG should only take a single
iteration. A random multivector is used to initialize the problem, the
problem is projected onto the subspace spanned by this multivector, the Ritz
values are computed (they will all be one), the residual is computed (it
will be zero), and this random multivector will comprise the solution
eigenvectors.

A rule of thumb for debugging these eigenvalue problems is that, if the
residuals are "good" for the computed eigenvalues and eigenvectors, the
eigenvalue problem defined by the users' operators (as implemented) has been
solved. If the eigenvalues are not those that are expected, then it is
likely that one the following is the case:
* something is wrong with the user-provided operators
* nothing is wrong with the user-provided operators, but the eigenvalues
computed are not the ones that were desired.

Is there some other problem that you were experiencing which caused you to
investigate this trivial (A=id=B) example?

Chris

On Sun, Mar 9, 2008 at 12:47 AM, Davood Ansari <david.ansari at gmail.com>
wrote:

>
> Well after all
>
> I guess it is ok for the LOBPCG to yield eigen vectors that are linear
> combinations of the eigen-vectors which correspond to degenerate
> eigen values ? Is that so?
>
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