Re: Problem with Mathematica driving me nuts

*To*: mathgroup at smc.vnet.net*Subject*: [mg46804] Re: [mg46791] Problem with Mathematica driving me nuts*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Tue, 9 Mar 2004 04:30:47 -0500 (EST)*References*: <200403080910.EAA10442@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.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. > Thanks. > I assume you are using a version 4.something, as version 5 appears to do better (i.e. it gives x->2.). The code below was run in version 4.2. In[9]:= FindRoot[x^2 == 4x - 4, {x, 1}, AccuracyGoal->14, MaxIterations->200] Out[9]= {x -> 2.} InputForm will reveal that it is really only correct to 7 or so places, which is appropriate because you are at a double root (so accuracy will be roughly twice that, as requested). Note that the Automatic setting for AccuracyGoal will try to attain 6 decimal places in version 4. We see below that this was in fact accomplished. In[13]:= rt = FindRoot[x^2 - 4*x + 4, {x, 3}] Out[13]= {x -> 2.00098} In[14]:= Log[10, x^2 - 4*x + 4 /. rt] Out[14]= -6.0206 The other example gives a similar result. Daniel Lichtblau Wolfram Research

**References**:**Problem with Mathematica driving me nuts***From:*bpw67deletethis@hotmail.com (benwoodward.com)