Mike Day writes:
> Is the relatively low speed a necessary price
> for recent improvements in the robustness of
> p. in J6.01?
>
If you have a lot of quadratics to solve, using a special method
rather than p. will almost certainly be faster.

I have no idea how p. works: presumably it could use special case
analysis for the solutions in radicals (degree at most 4).  Finding
polynomial roots in general is a hard problem because of instability
issues: small changes in the coefficients can cause large changes in
the roots.  The celebrated example is Wilkinson's polynomial, referred
to in the release notes and described in more detail at:

http://en.wikipedia.org/wiki/Wilkinson's_polynomial

I regard p. for root finding as a useful first approximation, but I
would not rely on it in general.  For example, it is a poor way of
calculating eigenvalues, even though mathematically they are the roots
of the characteristic polynomial.

Best wishes,

John

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