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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: [mg65286] Re: [mg65260] sorting list of roots af a transcendental function
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Fri, 24 Mar 2006 00:59:43 -0500 (EST)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

a=200*Random[]

110.895

Duplicates can be removed with Union.

Union[
  Table[
    x/.FindRoot[Cot[x]==x/a-a/(4*x),{x,i}],
    {i,50}],
  SameTest->(Abs[#1-#2]<10^-6&)]

{3.03232,6.06528,9.09946,12.1354,15.1737,18.2148,21.2589,24.3065,27.3
576,30.\
4126,33.4713,36.5339,39.6003,42.6705,45.7443,48.8216}

However, the need for Union can be avoided by using better initial values for 
FindRoot

Table[
  x/.FindRoot[Cot[x]==x/a-a/(4*x),{x,i*Pi-0.1}],
  {i,50/Pi+1}]

{3.03232,6.06528,9.09946,12.1354,15.1737,18.2148,21.2589,24.3065,27.3
576,30.\
4126,33.4713,36.5339,39.6003,42.6705,45.7443,48.8216}

%==%%

True


Bob Hanlon

> 
> From: Dule <dule23 at gmx.de>
To: mathgroup at smc.vnet.net
> Subject: [mg65286] [mg65260] sorting list of roots af a transcendental function
> 
> 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?
> 2. How can i construct a list, where the values for x, which appear 
> multiple are dropped?
> 
> Thanks!
> 
> 


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