Karim Belabas on Mon, 05 Jul 2004 20:41:58 +0200 |
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Re: Polynomial Roots - how to interpret realprecision? |
* Gordon Royle [2004-07-05 13:01]: > I want to use "polroots" to calculate the roots of a large number of > *integer* polynomials. > > The documentation indicates that the precision is kept in the variable > realprecision.... and then it says > > ".. it is guaranteed to converge and to give the roots to the required > precision" > > Now, does this mean that the roots that are output are guaranteed > correct to that number of places? Yes. > From my (admittedly limited) understanding of the sensitivity of roots > of polynomials, I was under the impression that this would require some > intermediate calculations to be performed to a greater precision ... is > this so? This is so. A posteriori error estimates are made, and the computation is restarted ( with appropriate precision ) if the estimates do not guarantee the requested precision was obtained. See also http://www.math.u-psud.fr/~belabas/pari/doc/faq.html#root Karim. -- Karim Belabas Tel: (+33) (0)1 69 15 57 48 Dep. de Mathematiques, Bat. 425 Fax: (+33) (0)1 69 15 60 19 Universite Paris-Sud http://www.math.u-psud.fr/~belabas/ F-91405 Orsay (France) http://pari.math.u-bordeaux.fr/ [PARI/GP]