Starting values with FindRoot

• To: mathgroup at smc.vnet.net
• Subject: [mg20620] Starting values with FindRoot
• From: Benoit Carmichael <benoit at ecn.ulaval.ca>
• Date: Thu, 4 Nov 1999 02:13:33 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```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:

FindRoot[eq,x0]

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?

Benoit Carmichael
Professeur
Departement d'economique
Pavillon J.-A. de Seve
Cite Universitaire
Ste-Foy (Quebec)