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Re: Motion 6

Vincent Lefevre wrote:

On 2009-09-17 12:51:11 +0200, Arnold Neumaier wrote:

For rigorous multiple precision calculations, a triplex representation
is far superior in this respect, as - unlike a midrad representation -
it degrades gracefully when the interval gets wide, and allows the
representation of intervals like [1,inf], which the midrad
representation doesn't.
This is slower.
This is not much slower, since the multiprecision part takes the bulk of the computation time. 


So I wouldn't say it is superior. In some applications
(probably in particular those that are best with midrad), degrading
gracefully is not necessarily useful. For instance, when the error no
longer remains small, the results could be regarded as meaningless,
and recomputing the results with more precision may be necessary.


There is no clear marhgin when something becomes meaningless;
see the example from my previous mail
   x in 1e-10000 + [0,Inf], which encodes sign information,

This makes it important to have graceful degradation.


Arnold Neumaier