super
On Thursday, June 16, 2016 at 3:22:52 AM UTC-4, Simon Byrne wrote: > > I realise this is a bit late to the party, but in case anyone is still > interested (or happens to be searching in future), I've created: > https://github.com/simonbyrne/Remez.jl > > The code is mostly based on some code by ARM: > > https://github.com/ARM-software/optimized-routines/blob/master/auxiliary/remez.jl > but updated for newer Julia versions, and built into a package. > > On Tuesday, 17 June 2014 17:11:22 UTC+1, Hans W Borchers wrote: >> >> That is right. The Remez algorithm finds the minimax polynomial >> independent of any given prior discretization of the function. >> >> For discrete points you can apply LP or an "iteratively reweighted least >> square" approach that for this problem converges quickly and is quite >> accurate. Implementing it in Julia will only take a few lines of code. >> >> See my discussion two years ago with Pedro -- from the *chebfun* project >> -- about why Remez is better than solving this problem as an optimization >> task: >> >> http://scicomp.stackexchange.com/questions/1531/the-remez-algorithm >> >> You'll see that the Remez algorithm gets it slightly better. >> >> >> On Tuesday, June 17, 2014 5:12:21 PM UTC+2, Steven G. Johnson wrote: >>> >>> Note that Remez algorithm can be used to find optimal >>> (minimax/Chebyshev) rational functions (ratios of polynomials), not just >>> polynomials, and it would be good to support this case as well. >>> >>> Of course, you can do pretty well for many functions just by sampling at >>> a lot of points, in which case the minimax problem turns into an >>> finite-dimensional LP (for polynomials) or a sequence of LPs (for rational >>> functions). The tricky "Remez" part is finding the extrema in order to >>> sample at the optimal points, as I understand it. >>> >>
