Updated: January 22, 2004
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Tutorial: Validated Scientific Computing Using Interval Analysis

Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
Milwaukee, WI 53201-1881 USA
George.Corliss@Marquette.edu

This tutorial introduces interval beginners (e.g., graduate students and applications researchers) to concepts and patterns of interval analysis. We assume a first course in scientific computation typically including floating point arithmetic, error analysis, automatic differentiation, Gaussian elimination, Newton's method, numerical optimization, and Runge-Kutta methods for ODE's. At the conclusion of this tutorial, you should be able to

• Understand most of the how and why of interval algorithms,
• Define your own f to use in existing software,
• Read modern papers on validating algorithms,
• Adapt and extend them for your own use, and
• Write your own algorithms and papers.

Coverage in this tutorial is similar to a standard introduction to scientific computing:

• Arithmetic and errors - Interval Arithmetic,
• Linear systems,
• Nonlinear rootfinding,
• Bounding ranges of functions,
• Global optimization,
• Quadrature,
• Ordinary differential equations (ODEs and DAEs),
• Partial differential equations,
• Lessons learned, and
• References.

We will not finish all these topics. The tutorial will include a lecture with examples in MATLAB and Sun's Fortran 95 and a set of supervised, hands-on exercises.