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Re: Revised version of Level 1 text (draft)

Dan Zuras Intervals wrote:

	I am more interested in the 'natural' uses of set
	theoretic functions.  In the case of intersection,
	they seem to involve deriving an interval for which the
	properties of both operands are true.  In the Newton's
	iteration:

		given xx(k) & xmid (the midpoint of that
		interval, we compute:

		xx(k+1) = (xmid - f(xmid)/ffprime(xx(k)))
				\intersect xx(k)

	That is, we seek a new interval that is contained in
	BOTH the old interval & the image of that interval
	under Newton's map.


This is an intersection of bare intervals. decorations make sense only
for range computations, not for domain reductions, as here. Thus they are needed inside the computations of 
     f(xmid) [xmid must be an interval to take care of roundoff]
and
     ffprime(xx(k)),
to check the assumptions under which the interval newton formula holds,
but not for the other calculations in the above iteration.