CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM
                  UNIVERSITY OF COLORADO AT DENVER


TITLE:   Survey of Interval Analysis for Validated Computation

SPEAKER: Dr. George F. Corliss, Mathematics, Marquette University
         Milwaukee, Wisconsin, email: georgec@mscs.mu.edu

DATE:    Wednesday, October 19, 1994

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    2:30 pm (Refreshments served at 2:15 pm)

ABSTRACT: Hamming once said, ``The purpose of computing is insight, not
numbers.''  If that is so, then the speed of our computers should
be measured in insights per year, not operations per second.  One
key insight we wish from nearly all computing in engineering and
scientific applications is, ``How accurate is the answer?''
Standard numerical analysis has developed techniques of forward and
backward error analysis to help provide this insight, but even the
best codes for computing approximate answers can be fooled.

In contrast, validated computation checks that the hypotheses of
appropriate existence and uniqueness theorems are satisfied.  The
validation methods:

   -   use interval arithmetic with directed rounding to capture
       truncation and rounding errors in computation, and

   -   organize the computations to obtain as tight an enclosure
       of the answer as possible.

There are several high-quality software environments supporting
interval analysis.  There are programs available for the validated
solution of most of the common problems of scientific computing
including linear and nonlinear systems, optimization, quadrature, 
ordinary and partial differential equations.  In each case, the
programs provide insight by yielding an interval within which the
correct answer is GUARANTEED (subject only to modeling errors or
programming bugs) to lie.  ODE's will be used as the setting for
illustrating validation methods.