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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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