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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