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