3 ms·
In automatic differentiation we depend on the fact that a closed form elementary solution exists even if we don't calculate it directly. For integration we nee
by konjin 6y ago
In automatic differentiation we depend on the fact that a closed form elementary solution exists even if we don't calculate it directly.
For integration we need to prove that such a object exists for each expression we want to integrate before we try integrating. Which as far as I'm aware is a problem equivalent to that solved by the Risch algorithm.
- adamnemecek 6y agoOK but that's not how automatic differentiation would work?
- ajuc 6y ago> For integration we need to prove that such a object exists for each expression we want to integrate before we try integrating. Can't we just integrate away and check if it's correct by differentiating it back? EDIT: oh, I guess that's why we need to be able to check for function equality :)
- konjin 6y agoIt's been over a decade since I studied it, but from memory you could also end up in infinite loops when you start generating the closed form solution if it doesn't exist. Which with as much hand waving as possible is ultimately equivalent to the computer function form auto integration would produce.