arbitrary precision linear algebra

[Ben123]

On Mar 2, 9:04 am, Arthur Mc Coy <1984docmc... at gmail.com> wrote:
> What do you mean by "arbitrary precision" ? Each method of calculating
> of something has its own precision...

If you are unfamiliar with arbitrary precision, I'm referring to
http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic

Suppose I find the eigenvalues of a matrix and the eigenvalues range
from 1 to 0.0001. This can be handled by numpy in Python because the
smallest eigenvalue is larger than then numerical precision of 1E-19.
However, if the range of eigenvalues is 1 to 1E-40, then I will need
to increase the precision of all calculations leading up to finding
the eigenvalues.

I am working with complex valued matrices and I expect to get real
eigenvalues back (based on the physics of the system). The precision
of numpy is apparent from the imaginary component of the eigenvalues I
find, currently 1E-19 or 1E-20. I need better precision for small
eigenvalues.

In case you are curious, the complex-valued matrices are 20x20.

Thanks