3 ms·
I hope someday to actually understand this. It seems to come up once a year or so, and each time I understand a bit more... so hopefully in a few years...
by sophacles 17y ago
I hope someday to actually understand this. It seems to come up once a year or so, and each time I understand a bit more... so hopefully in a few years...
- deleted 17y ago[deleted]
- frisco 17y agoIt's really just Newton's method for successive approximations: http://en.wikipedia.org/wiki/Newtons_method http://en.wikipedia.org/wiki/Newtons_method
- eru 17y agoAnd a very clever zeroth approximation.
- jacquesm 17y agoExactly, that's the key to the whole thing. After all if your first approximation is 'in the ballpark' you get a lot of precision in one go. Newtons method would run 'infinitely long' to reach an arbitrary precision, normally the cutoff is some acceptable error. By getting within the ballpark on the first try you can get within acceptable error with one more approximation step. (acceptable depends on the use of the result of course).
- Confusion 17y agoIf you Google for that magic number, you will find a large number of explanations, requiring various levels of understanding. No doubt there is one clear enough for you; perhaps stack a few of them.
- sophacles 17y agoGood tip, thanks -- now on to making my brain hurt!