# best polynomial approximation

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## best polynomial approximation

 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: [hidden email] +------------------------------------------------- ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: best polynomial approximation

 Hi, My understanding is that Chebyshev polynomials solve the minimax approximation problem.  If this correct, what you need is an algorithm to compute Chebyshev polynomial approximation. I have written an R function to do this.  See the attached code that contains the function and an example. Is this helpful? I am not sure if there are better algorithms in some R packages. Ravi. -----Original Message----- From: [hidden email] [mailto:[hidden email]] On Behalf Of Patrizio Frederic Sent: Monday, May 17, 2010 5:53 PM To: [hidden email] Subject: [R] best polynomial approximation 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: [hidden email] +------------------------------------------------- ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.