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1D Newton's search
Suppose we want to find the root of
(see Figure
13.4). If our current estimate of the answer is
, we can get a better estimate by drawing the
line that is tangent to at
, and find the
point where this line crosses the x axis. Since,
and
we have that
F
or

(13.30) 
which gives
.
We apply the same process and iterate on .
Figure 13.4:
A plot of
for
indefinite.

Frank Vanden Berghen
20040419