newtons method
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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