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The Mathematica Programmer: Interval Plotting and Global Optimization

Roman Maeder
Organization: Wolfram Research, Inc.
Department: Kernel Technology
Journal / Anthology

The Mathematica Journal
Year: 1999
Volume: 7
Issue: 3
Page range: 279-290

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.

*Applied Mathematics > Numerical Methods
*Wolfram Technology > Programming > Graphing and Plotting
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*The Mathematica Programmer: Interval Plotting and Global Optimization, Part 2   [in Articles]