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MathGroup Archive 2006

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Re: sorting list of roots af a transcendental function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65272] Re: [mg65260] sorting list of roots af a transcendental function
  • From: Pratik Desai <pdesai1 at umbc.edu>
  • Date: Thu, 23 Mar 2006 06:58:31 -0500 (EST)
  • References: <200603221113.GAA10232@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dule wrote:

>Dear group,
>
>for calculating a model i need values for x which are given by the 
>transcendental function Cot[x] == x/a - a/(4*x). a is a parameter 0<a<200.
>i obtained the roots with Table and FindRoot:
>Table[FindRoot[Cot[x] == x/a - a/(4*x), {x, i}], {i, 1, 50}]]
>
>I have two questions:
>1. Is there a better way to do this?
>  
>
Perhaps if you break up your code, the data set may be easier to 
handle/understand
Clear[expr,rootsinit,x,a]
expr[x_,a_]=Cot[x] == x/a - a/(4*x)
rootsinit[i_,a_]:=x/.FindRoot[expr[x,a],{x,i}]
TableForm[Table[rootsinit[1,a],{a,1,20}],TableHeadings->Automatic]
Here one may fix the initial point in the root search and find different 
roots for different values of a

>2. How can i construct a list, where the values for x, which appear 
>multiple are dropped?
>  
>
Union can get rid of the "repeating roots" for different initial points 
with a fixed
Table[rootsinit[i,3],{i,1,20}]//Union

>Thanks!
>
>  
>


Hope this helps

Pratik Desai
Wolfram Research



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