*Is there an implementation of the Remez algorithm in Julia,or is someone working on this?*
Sometimes it is important to have a (polynomial) *minmax approximation* to a curve or function (on a finite interval), i.e., an approximating polynomial of a certain maximum degree such that the maximum (absolute) error is minimized. A least-squares approach will not work. For example, given a hundred or more discrete points representing the Runge function on [-1, 1], package *CurveFit* will generate a polynomial of degree 10 that has a maximum distance of about 0.10..., while the true minimax solution will have a maximal distance of about 0.06... ! The Remez algorithm <http://en.wikipedia.org/wiki/Remez_algorithm> solves this problem applying an iterative procedure. As Nick Trefethen has once said about other implementations of this algorithm: "One can find a few other computer programs in circulation, but overall, it seems that there is no widely-used program at present for computing best approximations" The most reliable and accurate existing realization nowadays appears to be the one available in Trefethen's MATLAB toolbox *chebfun*, operating with Chebyshev approximations -- perhaps package *ApproxFun* would be a good starting point. I thought that Julia might be an appropriate scientific computing environment to realize an efficient and accurate version of the Remez algorithm. I am considering doing it myself, but would prefer if someone with a better command of Julia has already done this.
