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Re: FindRoot for the determinant of a matrix with a varying size

  • To: mathgroup at smc.vnet.net
  • Subject: [mg59747] Re: FindRoot for the determinant of a matrix with a varying size
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Fri, 19 Aug 2005 04:32:43 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 8/18/05 at 12:17 AM, wssaca at gmail.com (Wonseok Shin) wrote:

>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?

A small change to the definition for f fixes things

In[1]:=
f[(x_)?NumericQ] := 
    Det[Table[Exp[(i - j)/x]/x, {i, 2, 5, x}, {j, 2, 5, x}]]
    
In[2]:=
FindRoot[f[x] == 0.1, {x, 5}]

Out[2]=
{x -> 10.}
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