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Sharper and smaller error bounds for low precision scientific computing
المتدخلون) المتدخل) : Théo Mary (Pequan) With the rise of large scale, low precision computations, numerical
algorithms having a backward error bound of the form nu, for a problem
size n and a machine precision u, are no longer satisfactory. Indeed,
with half precision arithmetic, such algorithms cannot guarantee even
a single correct digit for problems larger than a few thousands. This
has created a need for error bounds that are both sharper and smaller.
In this talk, we will discuss recent advances towards this double
goal. We will present new error analyses to obtain probabilistic
bounds that are sharper on average, and new algorithms that achieve
much smaller bounds without sacrificing high performance.
Marc.Mezzarobba (at) nulllip6.fr