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RE: Problem with Mathematica driving me nuts

• To: mathgroup at smc.vnet.net
• Subject: [mg46811] RE: [mg46791] Problem with Mathematica driving me nuts
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Tue, 9 Mar 2004 04:30:55 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

>-----Original Message-----
>From: bpw67deletethis at hotmail.com [mailto:bpw67deletethis at hotmail.com]
To: mathgroup at smc.vnet.net
>Sent: Monday, March 08, 2004 10:10 AM
>To: mathgroup at smc.vnet.net
>Subject: [mg46811] [mg46791] Problem with Mathematica driving me nuts
>
>
>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.
>Thanks.
>

Reading Help saves the nuts:

"The default setting for AccuracyGoal is 10 digits less than
WorkingPrecision."


In[2]:= $MachinePrecision - 10
Out[2]= 6


Such:

In[3]:= FindRoot[x^2 == 4x - 4, {x, 1}, AccuracyGoal -> 16]
>From In[3]:=
FindRoot::"cvnwt": "Newton's method failed to converge to the prescribed 
accuracy after 15 iterations."
Out[3]= {x -> 1.99997}


In[4]:=
FindRoot[x^2 == 4x - 4, {x, 1}, AccuracyGoal -> 16, MaxIterations -> 30]
Out[4]= {x -> 2.}

In[5]:=
FindRoot[x^2 - 4*x + 4, {x, 3}, AccuracyGoal -> 16, MaxIterations -> 30]
Out[5]= {x -> 2.}

--
Hartmut Wolf