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Re: FindRoot behaving funny?

  • To: mathgroup at
  • Subject: [mg15822] Re: FindRoot behaving funny?
  • From: "W. K. Bertram" <wkb at>
  • Date: Fri, 12 Feb 1999 18:39:43 -0500 (EST)
  • Organization: Australian Nuclear Science and Technology Organisation
  • References: <79ebqo$>
  • Sender: owner-wri-mathgroup at

Doug Webb wrote:

> Hello,
>   This is a simplified example of I problem I have run into with
> FindRoot. Does anybody have any idea why it's doing what it is? And if
> so, how I can make it do what I want, or some other work around? Thanks
> for any info. Here's the example:
> define a function that takes one input, and outputs two results:
> r[x_] := {x, x^2}
> It does what's expected:
> r[4]
> {4,16}
> Now, find a solution using FindRoot:
> FindRoot[ r[x] == {5, 25}, {x, 2}]
> returns an error (rather than the obvious answer of x->5):
> FindRoot::"frnum":
>     "Function {{-3., -21.}} is not a length 1 list of numbers at {x}
> ={2.}."

The reason why mathematica can't handle your problem in that way becomes
apparent when you try for example;

         FindRoot[ r[x] == {5, 12}, {x, 2}]

Clearly there is no single x-value that solves this. In fact, in general
the equation r[x] == {r1,r2} has no solution. One way of making your
problem comprehensible to Mathematica is

      FindRoot[{r[x1][[1]]==5, r[x2][[2]]==25},{x1,2},{x2,2}]


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