Dear Ravi: Thanks for pointing out the homotopy methods. Coming from Mathematics I was always considering SINGULAR for such a task which is also providing results when the solution set is not isolated points, but an algebraic variety.
For single points, homotopy methods appear to be an effective approach. I am wondering if it will be worth to integrate Jan Verschelde's free PHCpack algorithm, see <http://www.math.uic.edu/~jan/>, as a package into R -- if there would be enough interest. Best regards, Hans Werner Borchers Ravi Varadhan wrote: > > Uwe, > > John's comment about the difficulties with finding polynomial roots is > even > more forceful for a system of polynomials. There are likely numerous > roots, > some possibly real, and some possibly multiple. Homotopy methods are > currrently the state-of-art for finding "all" the roots, but beware that > they are very time-consuming. For locating the real roots, I have found > that a relatively simple approach like "multiple random starts" works > failrly well with a root-finder such as dfsane() in the "BB" package. > However, I don't know of any tests to check whether I have found all the > roots. > > Ravi. > > ---------------------------------------------------------------------------- > ------- > > Ravi Varadhan, Ph.D. > > Assistant Professor, The Center on Aging and Health > > Division of Geriatric Medicine and Gerontology > > Johns Hopkins University > > Ph: (410) 502-2619 > > Fax: (410) 614-9625 > > Email: rvarad...@jhmi.edu > > Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html > > -- View this message in context: http://www.nabble.com/newtons-method-tp23498698p23535875.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.