Grinnell's Law of Labor Laxity:
At all times, for any task, you have not got enough done today.
-- from Unix fortune
I spent the morning thinking about thermoelastic problems, then went to PDE lecture in the early afternoon, and then worked on my presentation for the matrix computations seminar tomorrow. I'm re-running some of my experiments now, and I was surprised to find that some of my work to correct subtle numerical difficulties in my code also made the code run faster. Usually there is a trade between speed and stability. The suspicious side of my nature sees a silver lining and wonders where the attached thunder cloud is hiding.
There was a lot of mail on the 754R floating point committee mailing list about
stochastic rounding. The idea with stochastic
rounding is to round and random. Authors of similar schemes in the past made grandious (and erroneous) claims about how probabilistic
error analysis significantly enhanced reliability and made conventional error analysis unnecessary. The proponents of stochastic rounding write
that their scheme differs significantly from probabilistic error analysis, but I'm not sure I see how different the spirit is. Floating point arithmetic
is not exactly real arithmetic, but neither is it fuzzy. It has precise rules, and it's possible to take use those rules to do remarkable things.
But more people learn a little about significant figures and standard normal distributions than learn about floating point arithmetic, so perhaps it's
not so surprising to find people who think floating point arithmetic is just real arithmetic with fuzz.
I should probably get back to my slides, now.
- Currently drinking: Red tea