From: Richard Fateman <fateman@be...>  20140707 22:04:29

On 7/7/2014 12:54 PM, Raymond Toy wrote: >>>>>> "Stavros" == Stavros Macrakis <(Σταῦρος Μακράκης)" <macrakis@...>> 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 JenkinsTraub 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. This is a current research topic. (Not JenkinsTraub, but rootfinding methods). Given that you cannot necessarily evaluate a polynomial accurately, it can be difficult to find its roots accurately. There are methods that find all roots at the same time, perhaps more accurately and more slowly. > > 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 > > > >  > Open source business process management suite built on Java and Eclipse > Turn processes into business applications with Bonita BPM Community Edition > Quickly connect people, data, and systems into organized workflows > Winner of BOSSIE, CODIE, OW2 and Gartner awards > http://p.sf.net/sfu/Bonitasoft > _______________________________________________ > Maximadiscuss mailing list > Maximadiscuss@... > https://lists.sourceforge.net/lists/listinfo/maximadiscuss 