Re: [R] Solving 100th order equation

From: Robert A LaBudde <ral_at_lcfltd.com>
Date: Sat, 24 May 2008 11:00:07 -0400

At 07:58 AM 5/24/2008, Duncan Murdoch wrote:
>Shubha Vishwanath Karanth wrote:
>>To apply uniroot I don't even know the interval values... Does
>>numerical methods help me? Or any other method?
>>
>
>I forgot: we also have polyroot().
>Duncan Murdoch
>>Thanks and Regards,
>>Shubha
>>
>>-----Original Message-----
>>From: Duncan Murdoch [mailto:murdoch_at_stats.uwo.ca] Sent: Saturday,
>>May 24, 2008 5:08 PM
>>To: Shubha Vishwanath Karanth
>>Subject: Re: [R] Solving 100th order equation
>>
>>Shubha Vishwanath Karanth wrote:
>>
>>>Hi R,
>>>
>>>
>>>
>>>I have a 100th order equation for which I need to solve the value
>>>for x. Is there a package to do this?
>>><snip>

Finding all of the roots of a 100-th order polynomial on a computer is not an easy task. It would take move than 100 digits of precision to do so. A similar problem to finding all 100 eigenvalues of a 100x100 ill-conditioned matrix.

The suggestion to use graphics to find small intervals localizing the roots of interest first would make the most sense, at least for the real roots.

It is highly unlikely that all 100 roots are needed. Usually the ones of interest are the one with the largest real part, or the ones inside the unit circle, or the real roots, etc.

Is this a homework problem?



Robert A. LaBudde, PhD, PAS, Dpl. ACAFS e-mail: ral_at_lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
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