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Starting values with FindRoot

  • To: mathgroup at
  • Subject: [mg20620] Starting values with FindRoot
  • From: Benoit Carmichael <benoit at>
  • Date: Thu, 4 Nov 1999 02:13:33 -0500
  • Sender: owner-wri-mathgroup at

I am fairly new to Mathematica. I have to solve numerically a large set 
of nonlinear equations. My question is: How can I set the starting 
values without having to explicitly name every variable? Here is an 
example of what I mean: Suppose I try to solve numerically the following 
two equations:
eq = Table[z[i]\^2 == 2  i, {i, 2}]

It would be nice if starting values could be set as a List. Example:

x0 = Table[{z[i], i +  .5}, {i, 2}]

and to solve the equations with the following statement:


Unfortunetly, it does not work. Mathematica does not seem to accept 
starting values as lists. The problem appears to be the outer {}. In 
place of x0 above, Mathematica looks for something like 
{z[1],1.5},{z[2],2.5}, while x0={ {z[1],1.5},{z[2],2.5} }. There is an 
extra set of {}.

I have found a solution by using a chain of  FullForm[], ToString[], 
StringDrop[] and ToExpression[]. Here is my solution:

ToExpression[ToString[FindRoot] <> "[" <> ToString[FullForm[eq]] <> "," 
    StringDrop[StringDrop[ToString[x0], 1], -1] <> "]"]

Althought this works OK, it is nevertheless a very roundabout way of 
doing a simple thing. Anyone knows a more elegant way of doing this?

Thanks in advance

Benoit Carmichael
Departement d'economique
Pavillon J.-A. de Seve
Cite Universitaire
Ste-Foy (Quebec)
Canada, G1K 7P4
Tel.: (418) 656-2131 #5442

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