Chebyshev approximations.

[Andrea Riciputi]

On Sunday, Jun 8, 2003, at 19:13 Europe/Rome, Brian Gough wrote:

> Andrea Riciputi writes:
>> Reading the reference manual's chapter about Chebyshev
>> approximation it's not clear (at least to me) how the c_n are
>> defined. In particular I've found out that I've to double all the
>> coefficients I've calculated by my own, in order to get
>> gsl_cheb_eval to work properly.  My c_n definition is: c_n = k
>> \int{0}{\pi} f(x) \cos(n x) dx where k = 2/pi if n != 0 and k =
>> 1/pi if n == 0. Given these definitions the series expansion is:
>> f(x) = \sum{k = 0}{N} c_k cos(k x) Where am I wrong?
>
> I think it's a bug -- the implementation is different from the
> definition given in the manual, there is a factor of 0.5 which needs
> to be moved from the eval function to the init function.
>
> Brian

Probably the bug was in my own code. I reworked it out and now 
everything seems to work smoothly. GSL implementation, according to 
Numerical Recipes, is good. Sorry for the mistake.

Cheers,
Andrea.

---
Andrea Riciputi

"Science is like sex: sometimes something useful comes out,
   but that is not the reason we are doing it" -- (Richard Feynman)