🚀 go-pugleaf

In article <13450@mentor.cc.purdue.edu>
	hrubin@pop.stat.purdue.edu (Herman Rubin) writes:

>> At last, something we agree on! But I confess that I have not used it
>> extensively, so I am prepared to believe that it may have utility I am
>> not personally cognizant of. Interval techniques will have to be
>> deployed in large quantities before it can be counted out of the
>> running, IMHO.

>Interval techniques will often be needed when extreme accuracy is needed. 
>But in these case, it will probably be necessary to use multiple precision
>anyway. 

Interval arithmetic is useful when robustness is necessary. For example,
in a paper "On Ray Tracing Parametric Surfaces" (D. L. Toth, SIGGRAPH '85
Conference Proceedings) interval arithmetic is used to reliably find the
nearest intersection beween a line and a parametric surface.

>There are cheaper ways to analyze errors in most situations than
>interval arithmetic, but they involve using various precisions.  In some
>cases, a very good estimate can even be made in advance of any computation.

Error estimation is not enough for robust computation, but, error bounding
by interval arithmetic is useful. As in Toth's paper, it is possible to use
non-interval newton iteration if its unique convergence is assured by
interval arithmetic.

						Masataka Ohta