arbitrary precision linear algebra

[Arthur Mc Coy]

On Mar 2, 5:26 pm, Ben123 <ben.is.loca... at gmail.com> wrote:
> 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 tohttp://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

You probably have to change the method of finding eigenvalues.
Which one do you use? Power or algebraic ?
Do you use Gaussian method to simplify matrices ?

Languages can't support infinitely large or small numbers, so try to
multiply the inner variables by 10^n to increase their values if this
will not involve on the method. For example, I did this when was
calculating geometric means of computer benchmarks.
In such way you will be storing the number of zeros as n.

Yes, interesting what are you calculating.