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## [Axiom-math] Re: symbolic interval algorithms

 From: G. William Walster Subject: [Axiom-math] Re: symbolic interval algorithms Date: Sat, 18 Feb 2006 12:43:40 -0800 User-agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.7) Gecko/20040616

Yes.  Continued fractions are often used for computing arbitrary
precision point results.  This kind of work can be useful when
developing high precision library routines for computing special
functions.  However, most engineering problems require the use of
intervals to bound uncertainty in measured inputs.  Most practical
computations do not have infinitely precise inputs.  For example,
take a look at the NIST page
<http://physics.nist.gov/cuu/Constants/index.html>

We both have plenty of work to do. :)

Cheers,

Bill

root wrote:

just checked my book pile and i have moore's interval analysis book.
most of the interval research work i did got shelved when i left ibm research in 95. i haven't yet found the box containing my
research notes but it's certainly in the pile.

a separate thread that has had some discussion on the axiom mailing
list is the use of exact-real arithmetic. axiom can represent exact-reals
as "infinite partial fractions". these infinite partial fractions are
numbers that are represented essentially as a "stream" where finitely
many elements are computed and the rest are represented as a continuation
function.

axiom uses these infinite objects in a variety of ways. essentially you
only call the continuation function when you need to display more digits
in the final result.

so it might be interesting to try to combine the interval example
(N-R iteration) with exact-real endpoints on the intervals.

t

ps:

i'm copying this to the address@hidden mailing list in case
anyone else is interested in the problem of adding intervals and
provisos to axiom.
bill is the co-author of "Global Optimization Using Interval Analysis"
ISBN 0-8247-4059-9