# [R] best polynomial approximation

Patrizio Frederic frederic.patrizio at gmail.com
Tue May 18 23:38:02 CEST 2010

```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
>
> 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.
>>
>>
>> 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
>> +-------------------------------------------------
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> 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 at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> 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.frederic at unimore.it
+-------------------------------------------------

```