[R] best polynomial approximation

[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.
> 
> 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.frederic at unimore.it
> +-------------------------------------------------
> 
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