Of course, the 'real' solution is actual Numerical Analysis (as I'm sure you know) to keep the error properly bounded, but it's really interesting to have a sort of middle ground which just stabilizes the math locally... which might be good enough.
Other fun fact: Numerical Analysis is a thing that's really hard to imagine unless you happen to be introduced to it during an education. It's so obviously a thing once you've heard of it, but REALLY hard to come up with ex nihilo.
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That's a real "fun fact" kind of thing. Love it.
Of course, the 'real' solution is actual Numerical Analysis (as I'm sure you know) to keep the error properly bounded, but it's really interesting to have a sort of middle ground which just stabilizes the math locally... which might be good enough.
Other fun fact: Numerical Analysis is a thing that's really hard to imagine unless you happen to be introduced to it during an education. It's so obviously a thing once you've heard of it, but REALLY hard to come up with ex nihilo.