Dear colleagues, thank you so much for your help. Hans, I think the Remez algorithm is what I need. I will brush up on fortran language. Ravi, thanks anyway, I appreciated.
All the best, Patrizio On Tue, May 18, 2010 at 12:10 PM, Hans W Borchers <hwborch...@googlemail.com> wrote: > > 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. > -- +------------------------------------------------- | 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.
