Re: [Maxima-discuss] allroots precision

[Raymond T. <toy...@gm...>]

>>>>> "Stavros" == Stavros Macrakis <(Σταῦρος Μακράκης)" <mac...@al...>> writes:

    Stavros> ? allroots and ? bfallroots (unlike ? realroots) say
    Stavros> nothing about the precision of the result, or how to
    Stavros> control it (except the unhelpful "allroots may give
    Stavros> inaccurate results in case of multiple roots"). It would
    Stavros> be helpful if someone knowledgeable about the algorithms
    Stavros> could add some information about precision to the docs.

allroots (and bfallroots) use Jenkins-Traub to compute the
roots. AFAIK, there are no guarantees on accuracy. I do know accuracy
degrades for multiple roots (or near multiples). And since deflation
is used, the accuracy of the later roots is worse than the earlier
roots.

Having said that, I think the algorithm does produce a single root, r,
of the polynomial, P, such that |P(r)| < eps where eps is
approximately roundoff in computing the polynomial.

Ray