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The Mathematica Programmer: Interval Plotting and Global Optimization, Part 2

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

The Mathematica Journal
Year: 2000
Volume: 7
Issue: 4
Page range: 456-464

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. The first part of this paper can be found in The Mathematica Journal vol. 7, issue 3.

*Applied Mathematics > Numerical Methods
*Applied Mathematics > Optimization
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