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MathGroup Archive 1996

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Newton's Method Help [0/1]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5072] Newton's Method Help [0/1]
  • From: rligeski at webbernet.net
  • Date: Fri, 25 Oct 1996 22:48:17 -0400
  • Organization: WebNet
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,

    In my calculus class we just began using Mathematica for Newtons method.  
We were given a lab to do involving the method, but there is a special program 
so we can use Newton[] and NewtonTable[].  The former takes the equation with 
an initial guess goes through a certain number of iterations and then graphs 
each of them.  The latter does the same thing except it puts it into a table 
format instead of graphing.  I do understand Newtons method.  We were given 2 
problems that no one in my class can get.  He won't help us because he thinks 
we should be able to do it.  I was wondering if someone could help me with the 
problems.  They are:

1.  Find a polynomial F so that Newton's method fails to converge in the 
following way for X(sub 0)=1.  The first iteration gives X(sub 1)= -1, the next 
X(sub 2)= -2, and X(sub 3)=X(sub 0] the starting point.  Assume F(1)=1, 
F(-1)=2, and F(-2)=3

2.  Find a polynomial F which fails as above but which also has one root 
between -1 and 1 at 0; that is in addition to values given above, F(0)=0

    The teacher did give us a hint, he said sketch it first.  I did this but 
don't know how to use Mathematica well enough to do this.  I also searched the 
Mathematica website but that did not help.  I am going to include the notebook 
that we used in school, because this is not standard.  I would appreciate it if 
someone would try to help me.

Thank You,
Brian Ligeski



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