4 ms·
Yeah the condition number helps in simple cases (or when solving single linear systems), but things rapidly spiral once you start getting into solving stiff ODE
by mjhay 4y ago
Yeah the condition number helps in simple cases (or when solving single linear systems), but things rapidly spiral once you start getting into solving stiff ODEs, etc - to the point that only numerical specialists can judge it. I feel like there ought to be ways of dealing with these issues in a more fine-grained manner with better guardrails - something like a numeric-aware typesystem or automatic algorithmic scheme generator. Like I said though, maybe in 100 years.
- bodhiandphysics 4y agostiffness has nothing to do with fp numbers... stiff equations are just as hard to solve using arbitrary precision bigints since the issue is the limits of approximations of the integral.
- mjhay 4y agoThat's getting back to my point though - the integral is over measurable sets of reals, and we are approximating that with finite-difference floats. This is a complex problem with many guises.