[Rd] Homotopy package in R - Developmental help needed. Was: RE: [R] newtons method

[Ravi Varadhan]

Dear Hans,

Thanks for your interest in homotopy methods.  I have been looking at L.T.
Watson's HOMPACK suite (written in Fortran) for solving nonlinear systems
(finding all the roots).  This is available in netlib, and since it is
written in Fortran, it should be relatively easily interfaceable with R.  

http://www.netlib.org/hompack/

I have been meaning to ask for help from the R development group for help
with creating this package, but due to severe time constraints, have not
been able to do that.  But here it is now!  Hence, I am moving this to
r-develop mailing list.

I would love to get help from you and anyone else on translating HOMPACK
into an R package.  If you or anyone else is interested, please send me an
email.

Best,
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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-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Hans W. Borchers
Sent: Thursday, May 14, 2009 3:46 AM
To: r-help at r-project.org
Subject: Re: [R] 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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