Eigenmumbles

If I find an MEng student or undergrad with the right inclination – or in the unlikely event that I get a windfall of time of my own that isn’t eaten by other projects – I’d like to build a twist on the simple calculator language. I want a calculator that estimates rounding errors throughout a calculation based on the standard $(1+\delta)$ model, and uses sensitivity analysis to show how those rounding errors propogate through the calculation. This wouldn’t be all that much more complicated than the usual symbolic differentiation stuff. The only thing that’s different is that one would effectively be computing partial derivatives with respect to variables representing the rounding error committed at each step of the computation.

The cool thing about this is not that it would provide approximate a posteriori error bounds. I already know how to do that, and this tool wouldn’t really help with the hard part, which is doing an a priori analysis to reveal where problems are likely to occur, and then being clever in a way that guarantees adequate accuracy near those problem cases. No, the cool thing is that this could help my students understand what I mean when I talk about a single critical rounding error being amplified – without me walking through the error analysis at the board with them.