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MIMS

Desperately Needed Remedies for the Undebuggability of Large Floating-Point Computations in Science and Engineering

 

Gilbert Strang
William Kahan (University of California, Berkeley)
12th September 2011
2:00 pm. Alan Turing, Frank Adams Seminar rooms
Registration - to register for this event, please email Sebastian Rees.
Slides.

Abstract

If suspicions about the accuracy of a computed result arise, how long does it take to either allay or justify them?

Often diagnosis has taken longer than the computing platform's service life. Software tools to accelerate diagnosis by at least an order of magnitude could be provided but almost no scientists and engineers know to ask for them, though almost all these tools have existed, albeit not all together in the same place at the same time. These tools would cope with vulnerabilities peculiar to Floating-Point, namely roundoff and arithmetic exceptions.

But who would pay to develop the suite of these tools?

Nobody, unless he suspects that the incidence of misleadingly anomalous Floating-Point results rather exceeds what is generally believed. Ample evidence supports that suspicion.

William Kahan Biography

Prof. W. Kahan (now retired) error-analyzes scientific and engineering floating-point computations on electronic computers, which he has programmed since 1953.

Born and educated in Toronto, Canada, he spent two Post-doctoral years (1958-60) at Cambridge, England, before returning to teach at the University of Toronto until 1969, when he moved to the  University of California, Berkeley. Among his contributions are the infallible algorithms for the HP-12C financial calculator (still for sale since 1982), fast and accurate singular-value decompositions (with  G.H. Golub in 1964) now used very widely, and the mathematical foundation for the now near-ubiquitous IEEE Standard 754 for Binary (and later Decimal) Floating-Point.

Among his trophies are the ACM Turing Award (1989), S.I.A.M's Von Neumann Lecture (1997), and the IEEE Piore Award (2000).

 

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