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FindRoot for the determinant of a matrix with a varying size

• To: mathgroup at smc.vnet.net
• Subject: [mg59720] FindRoot for the determinant of a matrix with a varying size
• From: "Wonseok Shin" <wssaca at gmail.com>
• Date: Thu, 18 Aug 2005 00:17:48 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hello everyone,

I am a user of Mathematica 5.1 for Mac .
I defined the function using the determinant of a matrix of a varying
size.  Even though this function is  well-behaving, it seems that
FindRoot cannot deal this function.  Please look at the following code:

-------------------------------------------------
In[1]:=
f[x_] := Det[Table[Exp[(i - j)/x]/x , {i, 2, 5, x}, {j, 2, 5, x}]]

In[2]:=
Plot[f[x], {x, 3, 30}]
-------------------------------------------------

By running the above Plot command, you can see clearly that the
function f is very smooth in the interval 3< x < 30, and f[x] == 0.1
has a solution in 5 < x < 15.

But I've failed to find a solution of f[x] == 0.1 using FindRoot:

-------------------------------------------------
In[3]:=
FindRoot[f[x] == 0.1, {x, 5}]

Table::iterb : Iterator {i, 2, 5, x} does not have appropriate bounds.
-------------------------------------------------

Is there any workaround for this problem?

Thanks,

Wonseok Shin

• Follow-Ups:
  • Re: FindRoot for the determinant of a matrix with a varying size
    • From: Sseziwa Mukasa <mukasa@jeol.com>
  • Re: FindRoot for the determinant of a matrix with a varying size
    • From: Curtis Osterhoudt <gardyloo@mail.wsu.edu>