Maths error

[Hendrik van Rooyen]

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

[Tim Roberts]
> |> Actually, this is a very well studied part of computer science called
> |> "interval arithmetic".  As you say, you do every computation twice, once to
> |> compute the minimum, once to compute the maximum.  When you're done, you
> |> can be confident that the true answer lies within the interval.

>
> The problem with it is that it is an unrealistically pessimal model,
> and there are huge classes of algorithm that it can't handle at all;
> anything involving iterative convergence for a start.  It has been
> around for yonks (I first dabbled with it 30+ years ago), and it has
> never reached viability for most real applications.  In 30 years, it
> has got almost nowhere.
>
> Don't confuse interval methods with interval arithmetic, because you
> don't need the latter for the former, despite the claims that you do.
>
> |> 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...

- Hendrik