Re: Are there multiple roots?

In article <1156650930.680308.267980@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
carlos@xxxxxxxxxxxx writes:
Have you every thought about doing your root searching
via the Winding Number theorem and simply Cauchy integrals?
For Zeke polynomial, f(z) = (z-1)...(z-20). I compute in
double precision a winding number for an appropriately chosen
circular contour as (19.9999999999999, 1.424416140594076E-015).
Since we have a polynomial, the real part tells that we have
at most 20 roots.

By suitably deformation and translation of the contour, you can
find the roots. For z=1, I find



val = ( 1.00000000000000 , 3.174127627403323E-015)
z = ( 1.00000000000000 , 2.663980147588063E-015)


(snip)

and all coefficients can be fairly well represented as
double floats. By contrast, the mantissas of many of
coefficients of P60 suffer significant truncation when
chopped off to 16 places.

Well, of course! If you expand the polynomial such that the
coefficients can't be accurately represented in the precision
of the computation, then you're going to get the wrong answer.
Geez, this isn't rocket science.

--
Steve
http://troutmask.apl.washington.edu/~kargl/
.

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