Maths error

[Hendrik van Rooyen]

"Nick Maclaren" <nmm1 at cus.cam.ac.uk> wrote:

> Yes, but that wasn't their point.  It was that in (say) iterative
> algorithms, the error builds up by a factor of the base at every step.
> If it wasn't for the fact that errors build up, almost all programs
> could ignore numerical analysis and still get reliable answers!
> 
> Actually, my (limited) investigations indicated that such an error
> build-up was extremely rare - I could achieve it only in VERY artificial
> programs.  But I did find that the errors built up faster for higher
> bases, so that a reasonable rule of thumb is that 28 digits with a decimal
> base was comparable to (say) 80 bits with a binary base.
> 

I would have thought that this sort of thing was a natural consequence
of rounding errors - if I round (or worse truncate) a binary, I can be off
by at most one, with an expectation of a half of a least significant digit,
while if I use hex digits, my expectation is around eight, and for decimal
around five...

So it would seem natural that errors would propagate 
faster on big base systems, AOTBE, but this may be 
a naive view.. 

- Hendrik