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 ---------------------------------------------------------------------------- -------- -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Uwe Ligges Sent: Tuesday, May 12, 2009 9:23 AM To: John C Nash Cc: r-help@r-project.org Subject: Re: [R] newtons method John C Nash wrote: > Finding polynomial roots is not a problem where one wants a quick and > dirty code. There are a lot of pitfalls, especially if there are roots > that are multiples, and there has been a lot of work on this problem. > See http://en.wikipedia.org/wiki/Category:Root-finding_algorithms . > > And Uwe may not be aware that optim() is contra-recommended for > functions of 1 variable, Has anybody told us something about just 1 variable? uwe > which seems to be the problem here. But there is ?polyroot > > JN > > > Message: 130 > Date: Tue, 12 May 2009 11:12:51 +0200 > From: Uwe Ligges <lig...@statistik.tu-dortmund.de> > Subject: Re: [R] newtons method > To: Kon Knafelman <konk2...@hotmail.com> > Cc: r-h...@stat.math.ethz.ch > Message-ID: <4a093d93.1020...@statistik.tu-dortmund.de> > Content-Type: text/plain; charset=ISO-8859-1; format=flowed > > > > Kon Knafelman wrote: > >> > Hi, >> > > Does anyone know how to code newton's method for finding the >> > > roots >> of polynomial functions? im not sure whether i need to do this >> manually, or just code something with a loop to stop when it gets to >> the desired result >> > > See ?optim for optimization methods. > > Uwe Ligges > > ______________________________________________ > 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. ______________________________________________ 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. ______________________________________________ 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.