I guess you may be looking for the Remez algorithm. AFAIK there is no implementation in one of the R packages. You can find FORTRAN code in the Collected Algorithms of the ACM (no. 604) which probably could be called from R.
There appears to exist a discrete, equi-distant(?) version as function 'remez' in the signal package, if that is of any help to you. I have never used it. Regards, Hans Werner P.S.: The Chebyshev polynomials do not compute the "best polynomial approximation", but they provide a nice way to estimate the maximal distance to this best approximating polynomial. Patrizio Frederic wrote: > > Dear R-users, > I learned today that there exists an interesting topic in numerical > analysis names "best polynomial approximation" (BSA). Given a function > f the BSA of degree k, say pk, is the polynomial such that > > pk=arginf sup(|f-pk|) > > Although given some regularity condition of f, pk is unique, pk IS NOT > calculated with least square. A quick google tour show a rich field of > research and many algorithms proposed for computing such a task. > > I was wondered if some of you knows about some R implementations > (packages) for computing BSA. > > Many thanks in advance, > > Patrizio > > as usual I apologize for my fragmented English > > -- > +------------------------------------------------- > | Patrizio Frederic, PhD > | Assistant Professor, > | Department of Economics, > | University of Modena and Reggio Emilia, > | Via Berengario 51, > | 41100 Modena, Italy > | > | tel: +39 059 205 6727 > | fax: +39 059 205 6947 > | mail: patrizio.frede...@unimore.it > +------------------------------------------------- > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > -- View this message in context: http://r.789695.n4.nabble.com/best-polynomial-approximation-tp2220439p2221042.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.