[R] newtons method

Hans W. Borchers hwborchers at googlemail.com
Thu May 14 09:46:04 CEST 2009

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: rvaradhan at jhmi.edu
> Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

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