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! > >