Re: FindRoot for the determinant of a matrix with a varying size
- To: mathgroup at smc.vnet.net
- Subject: [mg59736] Re: [mg59720] FindRoot for the determinant of a matrix with a varying size
- From: Sseziwa Mukasa <mukasa at jeol.com>
- Date: Fri, 19 Aug 2005 04:32:04 -0400 (EDT)
- References: <200508180417.AAA08644@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On Aug 18, 2005, at 12:17 AM, Wonseok Shin wrote: > 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? The iterator in your definition of x produces more than one element only in the case 1 <= x <= 3, furthermore iterators must be specified over ranges of integers so a real valued x cannot be used. Since you suspect your solution lies between 5 and 15 (actually since for x > 3 the expression for f[x] simplifies to the one element matrix {{1/x}} the solution can be determined trivially) I would remove the dependence on x in the iterators of your expression. Regards, Ssezi
- References:
- FindRoot for the determinant of a matrix with a varying size
- From: "Wonseok Shin" <wssaca@gmail.com>
- FindRoot for the determinant of a matrix with a varying size