# [R] best polynomial approximation

Tue May 18 01:01:41 CEST 2010

```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.

I am not sure if there are better algorithms in some R packages.

Ravi.

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Patrizio Frederic
Sent: Monday, May 17, 2010 5:53 PM
To: r-help at r-project.org
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.

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.frederic at unimore.it
+-------------------------------------------------

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