# Talk on Accuracy and Stability at Cardiff

My previous post was about the launch meeting of SIAM Student Chapter at Cardiff, at which I gave the opening talk. My talk was titled Accuracy and Stability of Numerical Algorithms and covered rounding of (floating point) numbers, the interplay between precision and accuracy, higher precision computations, and the effect of tiny relative errors on performance profiles.

Here I describe four examples that I gave where rounding, or the choice of rounding mode, can have interesting or surprising (to some) effects.

• In 2006 Justin Gatlin was credited with a new world record of 9.76 seconds for the 100m. Almost a week after the race, the time was changed to 9.77 seconds, meaning that he had merely equalled the existing record held by Asafa Powell. The reason for the change was that his recorded time of 9.766 has incorrectly been rounded down to the nearest hundredth of a second instead of up as the IAAF rules require.
• In 2008 the Mail on Sunday got agitated by the possibility that whether or not the UK inflation target of 3% would be exceeded (and it was exactly 3% at the time) could depend on a change of one thousandth of a percent. They realized that since the inflation rate is published to one decimal place, a rate of 3.049 would round down to 3.0% but 3.050 would round up to 3.1% (since ties are rounded up in UK government calculations) and mean the target had been missed.
• In 1983 the Vancouver stock exchange found that its index had halved over the year since it had been founded. It turned out that the index had been rounded down after every calculation. When the index was recomputed (presumably with round to nearest, though my reference doesn’t say) it doubled.
• My telephone and cable provider, Virgin Media, wrote to me in 2007 with news about pricing. They had decreased the cost of my cable and line rental package. They had also changed the way calls charges are calculated by “rounding up to the next minute” instead of “charging to the nearest second” as before. They gave the example that “a call that lasts 4 minutes 50 seconds will be rounded up to 5 minutes”. What they didn’t mention is that a call that lasts 4 minutes 1 second will also be rounded up to 5 minutes!

The talk can be downloaded from my website: Accuracy and Stability of Numerical Algorithms.