🚀 go-pugleaf

In article <KHB.91Jun11185538@chiba.Eng.Sun.COM> khb@chiba.Eng.Sun.COM (Keith Bierman fpgroup) writes:
 > In article <9106120054.AA19903@ucbvax.Berkeley.EDU> jbs@WATSON.IBM.COM writes:
 >        3. The real problem with interval arithmetic is not that it's
 >    slow but that on real applications its error estimates are gener-
 >    ally so pessimistic as to be useless.
 > 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.
If we look at what the Karlsruhe people are doing there is no problem with the
error estimates from interval arithmetic.  To give an example: to solve a
system of linear equations, first a standard method is used to approximate
a solution.  Next, using interval arithmetic (plus dot product with one
rounding), in an iterative process the approximate solution is enclosed in
a solution interval that is made as small as possible.  I have seen from
the process where the lower and upper bound of each solution component
differed only in a single bit (and those bounds were guaranteed).
--
dik t. winter, cwi, amsterdam, nederland
dik@cwi.nl