Re: Testable Predictions by HdB

In article <54206$434511fb$82a1e3ad$23952@xxxxxxxxxxxxxxxx> Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:
> *** T. Winter wrote:
>
> > In article <55bd0$4343e91f$82a1e3ad$11927@xxxxxxxxxxxxxxxx> Han de Bruijn
> <Han.deBruijn@xxxxxxxxxxxxxx> writes:
> >
> > > Or do you trust the unrealistic upper bounds of ***'s error analysis and
> > > prepare for the worst case? (Well, provided that *** doesn't surprise me
> > > once again, I find them "unrealistic".)
>
> [ It's about Fibonacci Iterations in the neighbourhood of (1-sqrt(5)/2 ]
>
> > They are unrealistic, but it took me quite some time to find it. (I am
> > a bit rusty in my numerical analysis.)
>
> Rusty? Does that mean that you are out of business nowadays? :-(

Well, only in the beginning did I do numerical analysis, later I moved
on to numerical algebra, have gone to computational number theory, and
am now doing less theoretical stuff.

> > Convergence is linear with a
> > convergence factor of (2 - sqrt(5)). So once the iterates converge, they
> > will. You will find that at some initial guesses the relative error will
> > increase. (There would have been problems if the convergence had been
> > sub-linear.)
....
> There we find that x(k+1) = psi + eps , where eps < delta.psi^2 .
> Here psi = (1-sqrt(5))/2 therefore psi^2 = (3-sqrt(5))/2 . Right?
> Now I wonder if why that is not the same number as yours ...

Perhaps because I made an error in my calculations at 3:20 AM?
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

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