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Re: Find all roots with FindRoot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126258] Re: Find all roots with FindRoot
  • From: "djmpark" <djmpark at comcast.net>
  • Date: Fri, 27 Apr 2012 06:51:19 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <25227796.28036.1334923020612.JavaMail.root@m06> <10360915.126319.1335434220128.JavaMail.root@m06>

<< Ersek`RootSearch` 

RootSearch[(Tan[Sqrt[theta]] - 2*Sqrt[theta]/(1 - theta)) == 
  0, {theta, 0, 10000}, InitialSamples -> 3000] 

{{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}} 


David Park
djmpark at comcast.net 
http://home.comcast.net/~djmpark/index.html 



From: Mikael Anderson [mailto:mikael.anderson.1969 at gmail.com] 



I just wanted to give the RootSearch package a try but I wonder why
RootSearch misses some roots in the beginning of the solution when I change
the range as below:

>
> In[28]:= RootSearch[(Tan[Sqrt[theta]] - 2*Sqrt[theta]/(1 - theta)) ==
  0, {theta, 0, 1000}]

Out[28]= {{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}}

In[29]:= RootSearch[(Tan[Sqrt[theta]] - 2*Sqrt[theta]/(1 - theta)) ==
  0, {theta, 0, 10000}]

Out[29]= {{theta -> 0.}, {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





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