Re: Motion P1788/M0009.01_ExactDotProduct
On Tue, November 17, 2009 10:04, Ulrich Kulisch wrote:
>
> Roughly speaking: Without an exact dot product interval arithmetic is a
> nice toy. With it, it is a superior arithmetical tool.
Quite on the contrary, Interval arithmetic as it exists in manifold
implementations is a superior arithmetic tool already widely employed in
global optimization. and having a good reputation for solving a number of
challenging problems (though having a problematic reputation in a number
of other areas).
The widely used commercial global optimization package BARON won the
prestigious Beale-Orchard-Hayes prize of the Mathematical programming
society; its essential use of interval arithmetic (implemented without
exact dot product) is explicitly mentioned in the laudatio.
The top-ranked solution of the SIAM 100 digit challence solved half the
problems using multiprecision interval arithmetic, again without an exact
dot product.
The proof of the existence of the Lorentz attractor by Warwick Tucker
earned a
prize of the Eurpean Mathematical society, again with explicit mention of
interval arithmetic, and again without an exact dot product.
On the other hand, the exact dot product is only a nice toy, very little
used in applications that attracted sginificant attention outside the
interval community. The uses of the exact dot product outside of interval
applications only needs an accurately rounded dot product.
I therefore recommend that all voters vote No (and those who already voted
Yes change their vote to No), with a comment that their vote would change
to yes if instead of the exact scalar product an accurately rounded scalar
product would be recommended or required.
Arnold Neumaier