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I think you will be waiting a long time. I hope this helps elucidate why: https://math.stackexchange.com/questions/1635949/is-there-a-chain-rule-for-integratio
by hervature 6y ago
I think you will be waiting a long time. I hope this helps elucidate why:
https://math.stackexchange.com/questions/1635949/is-there-a-chain-rule-for-integration https://math.stackexchange.com/questions/1635949/is-there-a-...
- adamnemecek 6y agoThis assumes a little too much about how automatic differentiation would work.
- hervature 6y agoBased on the rest of your comments, I'm not sure you know that automatic differentiation is a well established technique that is 40+ years old.
- adamnemecek 6y agoBased on your comment, I'm not sure you know that dual numbers, the foundation of autodiff, is 150+ years old.
- hervature 6y ago> This assumes a little too much about how automatic differentiation would work. The use of 'would' implies that automatic differentiation has not been established. Also, if something is 40+ years old, then it follows that its foundation is even older.
- adamnemecek 6y agoI meant automatic integration.
- ogogmad 6y agoIntegration and differentiation are opposites: Integration is well behaved numerically, but poorly behaved algebraically. Differentiation is poorly behaved numerically, but well behaved algebraically. Therefore if one wants to do "automatic integration", one has to approach it in a radically different way to autodiff. And arguably, such a method does already exist; it's just very inefficient.
- srean 6y ago> Integration is well behaved numerically, but poorly behaved algebraically. > Differentiation is poorly behaved numerically, but well behaved algebraically. This is so pithy and true, am stealing that.