Sharper and smaller error bounds for low precision scientific computing

10/08/2019
Speaker(s) : 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.