Lecture 4.
Root Finding
Today we began our exploration of root finding
methods. The bisection method works by shrinking an interval that is known to
include at least one root. We discussed ways in which we can decide to terminate
the algorithm. The algorithm is simple to understand. It is also easy to argue
that because the interval is guaranteed to shrink by half at every iteration the
accuracy of the approximation improves by at least one binary bit at every
iteration.
We then moved to Newton's
root finding algorithm. We saw a geometric interpretation of the algorithm to
provide some insight as to what is going on. We also saw a couple of examples
that were catastrophic to Newton's algorithm. I have postponed giving precise
termination conditions for Newton's algorithm as this is a subtle issue and
there was insufficient time for it today.
Thursday morning I plan to go over
solutions for HW-1 and HW-2.
Posted: Tue - September 20, 2005 at 11:31 AM