]> Hi Diego, I looked at that page thanks a bunch! That was just what I was hoping for and it answered many of my questions. -Eric Diego Olivier Fernandez Pons wrote: > 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 e-07 and x4 = 1.0 > > exact values are > > x1 = 1 x2 = 1 x3 = 0.1 e-07 x4 = 1 > > The difference is only due to a 'bad' pivot succesfully detected and > therefore avoided. > > > Diego Olivier > > > ------------------- > To unsubscribe, mail caml-list-request@inria.fr Archives: http://caml.inria.fr > Bug reports: http://caml.inria.fr/bin/caml-bugs FAQ: http://caml.inria.fr/FAQ/ > Beginner's list: http://groups.yahoo.com/group/ocaml_beginners > ------------------- To unsubscribe, mail caml-list-request@inria.fr Archives: http://caml.inria.fr Bug reports: http://caml.inria.fr/bin/caml-bugs FAQ: http://caml.inria.fr/FAQ/ Beginner's list: http://groups.yahoo.com/group/ocaml_beginners