Example 1
In the first two
frames, we see the standard process moving from x0 to
x1.
You'll notice that x1 is further
from x* = 1
than x0 is. Even worse, x1 has
landed close enough
to a different solution, that Newton's Method becomes
trapped by that solution.
Now imagine that our application requires that we
find a positive solution to
the equation in question. As we see in the
animation, the sequence produced by Newton's Method will settle down, but to
the wrong solution!
Copyright c 1996 by Steve Hetzler
and Bob Tardiff Department of Mathematics
and Computer Science, Salisbury State University, Salisbury, MD 21801.