Re: Problems with FindRoot and recursive functions

• To: mathgroup at smc.vnet.net
• Subject: [mg89680] Re: Problems with FindRoot and recursive functions
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Tue, 17 Jun 2008 00:40:17 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <g35g0m\$9bv\$1@smc.vnet.net>

```Daniel Kuang Chen Liu wrote:

> I have a recursive function of the form
>
>>> x1[t_] := If[t < 0, {t, 1}, 0.5 + x1[t - 1]]
>
> which returns a list of length 2, and the first element has a root at t=0.5
>>> In[3]:= x1[0.5]
>>> Out[3]= {0., 1.5}
>
> I want to use FindRoot to determine t0 such that x1[t0][[1]] == 0, so I use
> the following code
>
>>> FindRoot[x1[t][[1]] == 0, {t, 0.5}]
>
> to which Mathematica complains
>
> During evaluation of In[6]:= FindRoot::nlnum: The function value
> {False} is not a list of numbers with dimensions {1} at {t} = {0.5}.
>
> It would much appreciated if someone could tell me what is wrong with the
> code.

Hi Daniel,

You just have to ensure that the function x1 is called for numeric
values only [1]. For instance,

x1[t_?NumericQ] := If[t < 0, {t, 1}, 0.5 + x1[t - 1]]
FindRoot[x1[t][[1]] == 0, {t, 0.5}]

{t -> 0.}

Regards,
- Jean-Marc

[1] "How do I write a function which evaluates only when the argument is
a number?"
http://support.wolfram.com/mathematica/kernel/features/evalwhennumber.html

```

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