Re: Comments on Special functions, Quaternions, Octonions

From: Hubert HOLIN (Hubert.Holin_at_[hidden])
Date: 2001-05-30 17:15:54

Paris (U.E.), le 30/05/2001

        Bonsoir

--- In boost_at_y..., Peter Schmitteckert (boost) <boost_at_s...> wrote:
> Salut,
> 
> On Tuesday 29 May 2001 12:24, you wrote:
> > Somewhere in the E.U., le 29/05/2001
> 
> Aha. Delocalized ?

                Actually i was posting from my day work. But for all 
practical purposes, this can effectively be considered delocalization 
:-(   .

> [...]
> >                The terminology may not be the correct one, but what I meant
> > was the following:
> >
> >                If I create a piecewise approximation to a function, say with
> > one definition on [0;1] and another on ]1;2], then there is a risk of
> > discontinuity at 1, and that's bad if what I intended to model was in
> > fact continuous. So instead I find one approwimation on [0;3/2],
> > another on [1/2;2], and interpolate between the two approximations on
> > [1/2;3/2] (which I called the "continuity" or "matching" zone). This
> > generalises readilly.
> >
> >                We get better (order-0) behaviour, at the cost of more
> > computation (especially in the matching zone).
> >
> 
> 
> Hmm, I thought that you won't have problems with of this kind sinc(x) ,
> --- this functions is just too friendly ---,  setting the first interval to
> |x| < pow( epsilon, 0.25 ) you still have a higher order correction below 
> epsilon.  But I just realized that for long double on my g++ 2.95.3 sin()
> seems to be unreliable in the last few bits and could cause some trouble.
>  
> Concerning atan(), you can get in big trouble :(
>  
> Amicalement
> Peter Schmitteckert

                OK, I'll post one version. This will need gradual tuning.

        Amicalement

                        Hubert Holin
                        Hubert.Holin_at_[hidden]