MathGroup Archive 2002

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FindRoot starting values

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34223] FindRoot starting values
  • From: Kyriakos <tuxedomoon at yahoo.com>
  • Date: Fri, 10 May 2002 03:05:05 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Dear all,

My problem is closely related to the following one,
just on a bigger scale. I want to numerically find the
solution to a 
system of equations.

Suppose that we define a vector of the unknowns
Q = Array[q, {3}]
which generates
{q[1], q[2], q[3]}
and a vector of starting values, say all equal to 0.1
Q0 = Table[0.1, {3}]

We also define three functions on the unknowns, say
for example
RHS = Table[Sum[(Q[[i]]^i)*(i^j), {i, 3}], {j, 3}]
which expands to the vector
{
q[1] + 2 q[2]^2 + 3  q[3]^3,
q[1] + 4 q[2]^2 + 9  q[3]^3,
q[1] + 8 q[2]^2 + 27 q[3]^3
}
and the vector of the constants (results), say
LHS={1,2,3}

The goal is to solve RHS==LHS.

If I use
FindRoot[RHS == LHS, {q[1], Q0[[1]]}, {q[2], Q0[[2]]},
{q[3], Q0[[3]]}]
i get the solution
{q[1] -> -0.5, q[2] -> 1., q[3] -> -0.550321}

In my problem, the dimension of Q and Q0 is large, and
I cannot input the starting values one-by-one. The
fact that the way FindRoot accepts them is not in a
list form does not allow anything of the form
FindRoot[RHS == LHS, Table[{q[i], Q0[[i]]}, {i,3}] ]
or anything similar that I have tried.

Do you have in mind a way of circumventing the
problem?

Thanks in advance,

Kyriakos

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