[Jprogramming] Roots robustness?

[Raul Miller]

On Thu, Jul 31, 2008 at 6:43 PM, Zsbán Ambrus <ambrus at math.bme.hu> wrote:
> On Fri, Aug 1, 2008 at 12:11 AM, Raul Miller <rauldmiller at gmail.com> wrote:
>> One way of getting an idea of the magnitude of numerical errors
>> is to find the polynomial values at the indicated roots
>>   err=: p. 1 {:: p.
>>   err _1 1 1
>> 2.22045e_16 _1.11022e_16
>
> That may work as a quick test, but I think there are special
> polynomials where you get incorrect coefficients even if you use the
> best possible floating-point approximation for the roots.

I would think that "numerical errors" would describe those cases
rather nicely.  But I do recognize that there are different kinds
of numerical errors.

-- 
Raul