Comment by beansbeansbeans
13 hours ago
You're totally correct, my writeup in that section definitely was not clear. I've updated the blog, hopefully it's better. I've also given you a shoutout in the end of the post in my edit log, if that's cool with you
Sure, thanks. I also saw this sentence, which was not there in the last version (I think):
> That is to say, with n nodes, gaussian integration will approximate your function's integral with a higher order polynomial than a basic technique would - resulting in more accuracy.
This is not really the case, Gaussian integration is still just interpolation on n nodes, but the way of choosing the nodes increases the integration's exactness degree to 2n-1. It's actually more interesting that Gaussian integration does not require any more work in terms of interpolation, but we just choose our nodes better. (Actually, computing the nodes is sometimes more work, but we can do that once and use them forever.)