SIAM Workshop
Toronto, Canada, May 23-25, 2002

(including a special session honoring Ray Moore)

Immediately following the Seventh SIAM Conference on Optimization 
 (May 20-23, 2002) 
To be followed by a Fields Institute working group on optimization
 organized by Ken Jackson

Description and rationale (preliminary version)

Reliable computing is essential. There is no feasible alternative.
Modern societies rely more and more on computer systems.  Usually,
our systems appear to work successfully, but there are sometimes
serious, and often minor, errors. Ever increasing reliance on
computer systems brings ever increasing need for reliability.

Validated computing is one essential technology to achieve increased
software reliability.  Validated computing uses controlled rounding
of computer arithmetic to guarantee that hypotheses of suitable
mathematical theorems are (or are not) satisfied.  Mathematical
rigor in the computer arithmetic, in algorithm design, and in program
execution allow us to guarantee that the stated problem has (or does
not have) a solution in an enclosing interval we compute.  If the
enclosure is narrow, we are certain that we know the answer reliably
and accurately.  If the enclosing interval is wide, we have a clear
warning that our uncertainty is large, and a closer study is demanded.

Intervals capture uncertainly in modeling and problem formulation,
in model parameter estimation, in algorithm truncation, in operation
round off, and in model interpretation.

The techniques of validated computing have proven their merits in many
scientific and engineering applications including medical diagnosis
and treatment, financial simulation, mechanical design, oil reservoir
simulation, aeronautics, high energy particle accelerators,
engineering, chemical process simulation and control, computer graphics
for motion picture special effects, astrophysics, and many more.  They
help answer questions from, "How much irrigation water does a desert
golf course return effectively unused to its bordering stream?"
to "Will a near earth asteroid hit the earth, possibly ending life as we
know it?". 

The techniques of validated computing rest on solid and interesting
theoretical studies in mathematics and computer science.  Contributions
from fields including real, complex and functional analysis, semigroups,
probability, statistics, fuzzy logic, automatic differentiation,
computer hardware, operating systems, compiler construction, parallel
processing, and software engineering are all essential.

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