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## Re: [Help-gsl] how does cheb_eval_e work?

**From**: |
Brian Gough |

**Subject**: |
Re: [Help-gsl] how does cheb_eval_e work? |

**Date**: |
Fri, 5 May 2006 19:14:43 +0100 |

KL Tah writes:
>* Does anyone happen to know what the math is behind cheb_eval_c and how *
>* it calculates error bounds? Does it have anything to do with the *
>* minimax theorem? If so, how does the statement of this theorem relate *
>* specifically to the code given in cheb_eval.c?*
The general idea is sum of the rounding errors on each term, plus the
error in the approximation itself (magnitude of the last term).
For simplicity, the actual way gsl_cheb_err is calculated is an
overestimate computed at the end of the range +/-1, i.e. sum |c_i|
Lookt at it gsl_cheb_eval_mode_e is inconsistent with that as it just
takes the rounding error on the final result. I'll make a note to fix
that for the next release.
--
Brian Gough
Network Theory Ltd,
Publishing the GSL Manual - http://www.network-theory.co.uk/gsl/manual/