Re: Find all roots with FindRoot

*To*: mathgroup at smc.vnet.net*Subject*: [mg126284] Re: Find all roots with FindRoot*From*: Mikael Anderson <mikael.anderson.1969 at gmail.com>*Date*: Sun, 29 Apr 2012 02:06:40 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <25227796.28036.1334923020612.JavaMail.root@m06>

Actually I was using NSolve and was happy with that (see below). Then I happened to see the post on RootSerach and wanted to test it to see if I get the same results as NSolve. I got surprised that by increasing the range I did not get the same answer and hence posted the question. BTW Andrzej, do you see any advantage in using Reduce compared to NSolve? In[2]:= NSolve[(Tan[Sqrt[theta]] - 2*Sqrt[theta]/(1 - theta)) == 0 && 0 <= theta <= 10000, theta] Out[2]= {{theta -> 0.}, {theta -> 5.43413}, {theta -> 35.4046}, {theta -> 84.7952}, {theta -> 153.896}, {theta -> 242.729}, {theta -> 351.298}, {theta -> 479.605}, {theta -> 627.65}, {theta -> 795.435}, {theta -> 982.958}, {theta -> 1190.22}, {theta -> 1417.22}, {theta -> 1663.96}, {theta -> 1930.44}, {theta -> 2216.66}, {theta -> 2522.62}, {theta -> 2848.31}, {theta -> 3193.75}, {theta -> 3558.93}, {theta -> 3943.84}, {theta -> 4348.49}, {theta -> 4772.89}, {theta -> 5217.02}, {theta -> 5680.89}, {theta -> 6164.5}, {theta -> 6667.85}, {theta -> 7190.94}, {theta -> 7733.77}, {theta -> 8296.34}, {theta -> 8878.64}, {theta -> 9480.69}} /Mikael. On Sat, Apr 28, 2012 at 11:27 AM, Andrzej Kozlowski <akozlowski at gmail.com>wrote: > > Is there any reason why you don't want to use Reduce: > > In[166]:= > Reduce[(Tan[Sqrt[theta]] - 2*Sqrt[theta]/(1 - theta)) == 0 && > 0 <= theta <= 10000, theta] // N > > > theta == 0. || theta == 5.43413 || theta == 35.4046 || > theta == 84.7952 || theta == 153.896 || theta == 242.729 || > theta == 351.298 || theta == 479.605 || theta == 627.65 || > theta == 795.435 || theta == 982.958 || theta == 1190.22 || > theta == 1417.22 || theta == 1663.96 || theta == 1930.44 || > theta == 2216.66 || theta == 2522.62 || theta == 2848.31 || > theta == 3193.75 || theta == 3558.93 || theta == 3943.84 || > theta == 4348.49 || theta == 4772.89 || theta == 5217.02 || > theta == 5680.89 || theta == 6164.5 || theta == 6667.85 || > theta == 7190.94 || theta == 7733.77 || theta == 8296.34 || > theta == 8878.64 || theta == 9480.69 > > It gives you the complete answer (provably so) without the need to fiddle > with any options and is pretty fast too. Why do you need an external > package for this sort of thing? > > Andrzej Koz=C5=82owski > > >