Volume 7, Issue 3
Interval arithmetic provides a way of extending the action of elementary functions from points to intervals. It uses directional rounding to assure that for a point x and an interval i, f(x) lies in f(i) whenever x lies in i. It is closely related to Mathematica's ordinary arbitrary-precision arithmetic but its emphasis is on obtaining global results, not on high-precision computation. Two applications, interval plots and global minimization, show some of the results obtainable with interval arithmetic. Along the way, we encounter various data structures for stacks and priority queues.
Dr. Roman Maeder is one of the developers of Mathematica
responsible for elements of the programming language and details of internal
implementations. After several years as professor of computer science at ETH
Zurich he is now the founder and owner of MathConsult Dr. R. Mäder, a
consulting business specializing in computer-aided mathematics, especially for
the finance sector. The Mathematica Programmer is an on-going series of
articles about various programming topics. Earlier articles in this series are
available in expanded form in two books, The
Mathematica Programmer and The Mathematica Programmer II.