[Mplapack-devel] Can I compute eigenvalues of ill-conditioned matrix less than 10^-156 ?

[Gang Y. <ee...@gm...>]

Dear Folks,

   Many thanks to Mpack. It is really helpful for computing ill-conditioned
problems.

   Now I have a problem when I calculate the eigenvalues of an extremely
ill-conditioned matrix, in a problem of control system research. The matrix
is not very large, e.g., 30X30, but extremely ill-conditioned, i.e., having
the largest eigenvalue ~10^-2 and the smallest eigenvalue > 10^-156. I found
that the eigenvalue programme using GMP or MPFR can only compute eigenvalues
<10^-156, or I will get some minus eigenvalues which is not wrong because
the matrix is positive-definition. I use a 64-bit notebook.

   Any suggestions or comments? Thanks in advance.

best,
gang