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MathGroup Archive 2007

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Re: Iterating List

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77096] Re: Iterating List
  • From: "R.G" <gobiithasan at yahoo.com.my>
  • Date: Sun, 3 Jun 2007 06:13:44 -0400 (EDT)
  • References: <f3ltcf$5df$1@smc.vnet.net><f3og49$p9d$1@smc.vnet.net>

On Jun 1, 2:59 pm, Jean-Marc Gulliet <jeanmarc.gull... at gmail.com>
wrote:
> Gobiithasan wrote:
> > Hi, it would be a great help if Mathsgroup members can
> > show me how to code the following problem in
> > mathematica:
>
> > Say I have a function defined as:
> > f[a_, b_] = Integrate[Sin[x] + 3, {x, a, b}]
>
> > I can find b with given constant=2 and initial
> > value=0:
> > In[1]:=
> > Initialvalue = 0;
> > s1 = FindRoot[f[0, unknown] == 2, {unknown,
> > Initialvalue}];
> > x1 = Part[s1, 1, 2]
>
> > Now, using the x1 value obtained from FindRoot, I can
> > find x2:
> > s2 = FindRoot[f[x1, unknown] == 2, {unknown,
> > Initialvalue}];
> > x2 = Part[s2, 1, 2]
>
> > How can i do it for n times (to get xn in a list form)
> > with given initial value as:
> > initialvalue= {initialvalue1,initialvalue2,
> > ....,initialvalue3}
>
> > whereby each xi will get initialvalue[[i]].
>
> > Thanking you in advance
>
> > ~gobiithasan
>
> One possible way of doing what you are looking for is the use a
> functional construct such as NestList and a pure function (that why you
> can see #1 and &). For instance,
>
> In[1]:= f[a_, b_] = Integrate[Sin[x] + 3, {x, a, b}];
>    With[{Initialvalue = 0, n = 5},
>      Rest[NestList[FindRoot[f[#1, unknown] == 2,
>                {unknown, Initialvalue}][[1, 2]] & , 0, n]]]
>
> Out[1]= {0.607102, 1.13938, 1.64271, 2.15069, 2.69881}
>
> Regards,
> Jean-Marc

Hi Jean-Marc,
Thank you for your answer. The code you wrote works for
Initialvalue=0.
However, If I have initial values in terms of a list, say,
initialvalues=Table[t,{0,1/n}], How do i modify it?
Best Regards,
R.G



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