This is the mail archive of the
gsl-discuss@sources.redhat.com
mailing list for the GSL project.
Re: Chebyshev approximations.
- From: Brian Gough <bjg at network-theory dot co dot uk>
- To: Andrea Riciputi <ariciputi at pito dot com>
- Cc: Gnu Scientific Library <gsl-discuss at sources dot redhat dot com>
- Date: Sun, 8 Jun 2003 18:13:44 +0100
- Subject: Re: Chebyshev approximations.
- References: <2BD1DC74-9697-11D7-8817-000393933E4E@pito.com>
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