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Interval Plotting and Global Optimization, Part 1

Roman E. Maeder
MathConsult Dr. R. Mäder
Samstagernstrasse 58a
8832 Wollerau, Switzerland

maeder@mathconsult.ch
www.mathconsult.ch

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.

Intervals

Interval Plots

Three-Dimensional Plots

References

Additional Material


Converted by Mathematica      September 21, 1999