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MathGroup Archive 2005

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Re: 2 stage solution with FindRoot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57514] Re: 2 stage solution with FindRoot
  • From: dh <dh at metrohm.ch>
  • Date: Tue, 31 May 2005 04:59:05 -0400 (EDT)
  • References: <d76och$7pd$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Kuktar,
FindRoot searches roots numerically.
However, you request a solution to:
{x1,x2}={{x1,x2}|D[f1,x1]=0&&D[f2,x2]=0}
which depends on y1,y2. Therefore, this can only be done symbolically, 
because y1 and y2 are so far undetermined.
You write that "Solve" can not do it.
By stating D[f[x,y],x]==0 you are actually implicitely defining x as a 
function of y. In general there may be no closed form of x(y). Or the 
expression may be too complicated for Solve.
You could try "Reduce" and see if you get any further.

Otherwise, do you really need a two stage procedure? If not, you could 
do everything numerically in one go.

Sincerely, Daniel

mbekkali wrote:
> I have a function f[X1,X2], where X1 and X2 are vectors of variables
> x1[i] and x2[i], i=1,...,n. I need to solve the problem the following
> way. First, I need to solve for  X1={X1|D[f[X1,X2],X1]==0}.  Then,
> substituting X1 into f[.] I shall have f[X1[X2],X2]. I then need to
> solve for X2={X2|D[f[X1[X2],X2],X2]==0}.  Since function f[.] is very
> complicated Solve cannot handle it.  I have to use FindRoot.  I know I
> have to use symbolic solution to a numerical function but I do not know
> how exactly. I tried a couple of ways but have not succeeded. Please
> advise.
> 
> PS.  I want to make it clear that I need 2 stage solution, not just 1
> stage simultaneous solution to a set of 2n equations.
> 


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