compute eigenvalues for ill-conditioned matrix

[Powergon]

Hi fellows,

Currently I am using the LAPACK routine DSYEVR to compute the eigenvalues for a positive (all diagonal nonnegative) symmetric real matrix, but encountered with some questions. Can anyone give me some hints?

It's a small N*N matrix, with N only ~20. However, for some matrix, the DSYEVR gives even ridiculous results.
I observed that, for such matrix, the L1 condition number is larger than those giving expected results.
For example, when condition number is below 30, it gives expected results; when it goes to 80, it starts to give wrong
results, and when it goes to ridiculously large, say ~10^7, it gives very negative eigenvalues.

BTW, I only need the smallest eigenvalue.

So, I am wondering if there is any well-built routines or implementable methods for computing eigenvalues for ill-conditioned matrix.

Thank you very much!

[Powergon]

anyone give some hints? It's said that Lapack can handle ill-conditioned matrix. But it's wired that, for an ill-conditioned matrix, different eigensolvers give very different results..

What would be the problem?

Thanks a lot!