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