RE: [Camllist] Efficient and canonical set representation?
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Date:   (:) 
From:  Diego Olivier Fernandez Pons <Diego.FERNANDEZ_PONS@e...> 
Subject:  Re: [Camllist] Rounding mode 
Bonjour, > Somewhat off topic but why is this necessary from a numerical math > type of perspective. I am honestly curious as I don't see how this > would interact with the calculation in a meaningful way. You are right when you say that there are many sources of errors in numerical computations and that rounding errors are usually insignificant with respect to them. The point is that stochastic arithmetic (and its deterministic variant interval arithmetic) are useful to find where the accurancy of your computation is falling drastically (e.g. cancellations) I really haven't the place to explain extensively how CESTAC works but there are a few explanations in the ANP website http://anp.lip6.fr/cadna/Accueil.php (CADNA for C/C++ source codes, user's guide. Chapter 4. Survey of the CESTAC method. Many examples also on the homepages). The main idea is that in a first order approximation, the number of significant digits of a result can be estimated with respects to the dispersion of the different values it can take using several rounding modes. Then, you can avoid doing unstable computations like dividing by a small number (epsilon) very noised which makes you believe it is a good 'pivot' in a gaussian resolution, etc. The whole computation will then give a more accurate value. The website gives an example where usual gauss method finds x1 = 60 x2 =  8.9 x3 = 0.0 and x4 = 1.0 when you estimate the errors, you find x1 = 1.0 x2 = 1.0 x3 = 0.1 e07 and x4 = 1.0 exact values are x1 = 1 x2 = 1 x3 = 0.1 e07 x4 = 1 The difference is only due to a 'bad' pivot succesfully detected and therefore avoided. Diego Olivier  To unsubscribe, mail camllistrequest@inria.fr Archives: http://caml.inria.fr Bug reports: http://caml.inria.fr/bin/camlbugs FAQ: http://caml.inria.fr/FAQ/ Beginner's list: http://groups.yahoo.com/group/ocaml_beginners