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. >> >
