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MathGroup Archive 2004

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Re: Problem with Mathematica driving me nuts

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46824] Re: Problem with Mathematica driving me nuts
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Tue, 9 Mar 2004 04:31:14 -0500 (EST)
  • References: <c2he1m$ahd$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

bpw67deletethis at hotmail.com (benwoodward.com) wrote:
> FindRoot[x^2 == 4x - 4, {x, 1}]
>
> Out[4]=
> {x -> 1.99902}
>
> In[15]:=
> FindRoot[x^2 - 4*x + 4, {x, 3}]
>
> Out[15]=
> {x -> 2.00098}
>
> When the root is clearly two.
> Is Mathematica using Newton's Method like a Ti-92?
> Even if so, why wont it give a more accurate answer?
> I've tried N[%,30] but it doesn't do anything.
> I'm new to Mathematica coming over from a Ti-92, so everything is
> frustrating right now.

I'm surprised the answers you got were not more accurate. [I suppose you're
familiar with the fact that Solve and Reduce can be used to get the precise
answer.]

Using version 5.0.0:

In[1]:= FindRoot[x^2 == 4x - 4, {x, 1}]

Out[1]= {x -> 2.}

In[2]:= FindRoot[x^2 - 4x + 4, {x, 3}]

Out[2]= {x -> 2.}

The above outputs certainly _look_ nice. But FindRoot is a numerical
method after all, and so the values given are not precisely 2 :

In[3]:= FullForm[{%%,%}]

Out[3]//FullForm=
List[List[Rule[x,1.9999999701976776`]],List[Rule[x,2.0000000298023224`]]]

HTH,
David


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