4 ms·
Well, are there _any_ calculators out there that use Taylor expansions?
by rossant 2y ago
Well, are there _any_ calculators out there that use Taylor expansions?
- snovv_crash 2y agoI've done some work with fast approximate math libraries,and went down this path. Taylor was a dead-end, but Chebyshev polynomials work great. They have the nice property of having (close to) the minimum maximum (minimax) error over the entire range you are approximating.
- toolslive 2y agowell, from memory (this was > 20y ago) - Taylor gives you polynomial optimized for the evaluation of one point. - naive Newton gives you a polynomial with 0 error in the interpolation points [but the system has a bad condition] - Chebychev gives you a polynomial with minimal error over the interval of choice. So there is no real reason to ever use the Taylor series to approximate a function over an interval. The high school math teachers are lying.
- rmorey 2y agonot lying, probably just mistaken