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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 -

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