VALIDATED COMPUTING 2002 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, environmental 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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