Maths error

[Nick Maclaren]

In article <mailman.2768.1168930376.32031.python-list at python.org>,
"Hendrik van Rooyen" <mail at microcorp.co.za> writes:
|>
|> [ Interval arithmetic ]
|>
|> > |> For people just getting into it, it can be shocking to realize just how
|> > |> wide the interval can become after some computations.
|> >
|> > Yes.  Even when you can prove (mathematically) that the bounds are
|> > actually quite tight :-)
|> 
|> This sounds like one of those pesky:
|> "but you should be able to do better" - kinds of things...

It's worse :-(

It is rather like global optimisation (including linear programming
etc.)  The algorithms that are guaranteed to work are so catastrophically
slow that they are of theoretical interest only, but almost every
practical problem can be solved "well enough" with a hack, IF it is
coded by someone who understands both the problem and global
optimisation.

This is why the "statistical" methods (so disliked by Kahan) are used.
In a fair number of cases, they give reasonable estimates of the error.
In others, they give a false sense of security :-(


Regards,
Nick Maclaren.