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

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