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Re: Please listen to Ulrich here...

Dear Bill,
it may well be that CA and the EDP are not well suited for solving problems which in general are NP-hard.
The usefulness and necessity of CA and the EDP for other problems, however, have repeatedly been shown in the literature. As examples I just refer here to three articles in the volume: U. Kulisch and H. J. Stetter: Scientific Computation with Automatic Result Verification, Computing Supplementum 6, Springer 1988. [1] Th. Ottmann, G. Thiemt, Ch. Ullrich: On Arithmetical Problems of Geometric Algorithms in the Plane. 
[2] R. Lohner: Precise Evaluation of Polymomials in Several Variables.
[3] H. C. Fischer, G. Schumacher, R. Haggenmueller: Evaluation of Arithmetic Expressions with Guaranteed High Accuracy.
CA and the EDP can, for instance, also be very useful for so called "Numerical Verification Methods" or "Computer-Assistsed Proofs". Such methods do not just compute bounds for the error of an approximate solution but also prove the existence of an exact solution within the computed bounds. Examples are: a partial differential equation or a system of linear or non linear equations. 

With best regards
Ulrich



Am 08.08.2013 19:09, schrieb G. William (Bill) Walster:

Not seeing a post with an example, may I conclude that there are none?

Cheers,

Bill


On 8/7/13 9:03 AM, G. William (Bill) Walster wrote:



Please provide one example of how an exact EDP can substantially
reduce the computed width of *any* interval computation in which none
of the inputs are degenerate intervals and therefore infinitely precise.

Thanks in advance,

Bill

On 8/7/13 2:24 AM, Dan Zuras Intervals wrote:

     Folks,

     When Ulrich talks about problems with exact dot product he has some
     experience in the matter.  More than the rest of us put together.
     If we are about to have a standard that admits the possibility of
     a member that CANNOT do an exact EDP, all our work will be wasted.
     Please consider rewording this document in Ulrich's favor this time.
     He is not just blowing smoke.  It is hard but it is necessary.  Or,
     at least if we make it so.

     Let's make it so.

     Yours,

                     Dan




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Prof. Ulrich Kulisch

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