[R] Solving 100th order equation

[Spencer Graves]

Robert A LaBudde wrote:
> 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.
And uniroot, polyroot or solve.polynom should provide marvelous starting 
values. 
>
> Is this a homework problem?
>
> ================================================================
> Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
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