Re: doubt regarding floating point arithmetic Rounding schemes/ Truncation schemes

http://www.math.cmu.edu/~shlomo/VKI-Lectures/lecture1/node5.html
and http://www4.ncsu.edu/~mtchu/Teaching/Lectures/MA529/chapter1.pdf are 
too mathematical

Robert Myers wrote:

> On 19 Nov 2003 22:49:59 GMT, [EMAIL PROTECTED] (Nick Maclaren) wrote:
>
>
> > In article <[EMAIL PROTECTED]>,
> > vc  <[EMAIL PROTECTED]> wrote:
> >
> > > Rounding schemes/ Truncation schemes
> > >
> > > The choice of schemes decides the max error and bias.
> >
> > Correct.
> >
> >
> > > Zero bias schemes on an average cause little error but there is a large 
> > > chance htat they might hav a bias too and not end up with an error of 
> > > zero. Am I right or wrong
> >
> > I am not quite sure what you mean, but I think that you are roughly
> > right.  Most zero bias schemes have no bias, assuming that the errors
> > are uniformly distributed.  True probabilistic (stochastic) rounding
> > has no bias, whatever the distribution of errors, but has twice the
> > mean square error and makes debugging slightly (!) harder.
>
> When I saw the subject line, I thought, now that will get a response
> from Nick.
>
> For extra credit, you might want to study
>
> http://www.cs.ucla.edu/~stott/mca/CSD-970014.ps.gz
>
> and the links to the literature it provides.  In any case, roundoff
> bias isn't likely to matter much one way or the other for
> poorly-conditioned problems:
>
> http://www4.ncsu.edu/~mtchu/Teaching/Lectures/MA529/chapter1.pdf
>
> http://www.math.cmu.edu/~shlomo/VKI-Lectures/lecture1/node5.html
>
> http://www.math.princeton.edu/~ellenber/Math204Lects/Week12.pdf
>
> but that probably isn't what the homework problem asked about. ;-).
>
> RM