4 ms·
>90% of numerical analysis would remain if continuous arithmetic was exact. There exist some prominent failures of finite precision arithmetic (and they resona
by jedbrown 8y ago
>90% of numerical analysis would remain if continuous arithmetic was exact. There exist some prominent failures of finite precision arithmetic (and they resonate with uninformed audiences), but discretization and modeling errors are far more insidious and a deeper challenge for reliable scientific computing.
- angry_octet 8y agoAgreed. Though I'd say that model errors are a challenge, but I wouldn't call them insidious. There is generally serious analysis of the effect of the chosen discretization method/grid size, how to handle sub-grid scale effects, etc. Likewise models. I think it is interesting to compare this old panic with ML work. Without gazillions of flops the neural network approach was dead. After a few years it became clear that float/double precision was useless, and now for certain problems half precision is standard. Where one resource (people, CPU, ram, money) is the fixed constraint, other factors will be tweaked to compensate.
- jedbrown 8y agoI don't know what domain you work in. The modest 1986 editorial statement from the Journal of Fluids Engineering is still pretty much a gold standard for rigor in real-world applications and is exceedingly rarely achieved in domains where direct observational data is hard to come by (most of geophysics, much of biophysics, etc.). E.g., https://jedbrown.org/files/20160912-NumericalAccuracy.pdf https://jedbrown.org/files/20160912-NumericalAccuracy.pdf