[R] newtons method

[Ravi Varadhan]

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.

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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 Uwe Ligges
Sent: Tuesday, May 12, 2009 9:23 AM
To: John C Nash
Cc: r-help at 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 <ligges at statistik.tu-dortmund.de>
> Subject: Re: [R] newtons method
> To: Kon Knafelman <konk2001 at hotmail.com>
> Cc: r-help at stat.math.ethz.ch
> Message-ID: <4A093D93.1020702 at 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
> 
> ______________________________________________
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