Hatem Ltaief - King Abdullah University of Science and Technology (KAUST) Linear algebra is at the core of scientific computing. Over the last two decades, it has witnessed great (r)-evolution with the hardware technology scaling and has had to constantly adapt to challenging landscapes of emerging architectures, while exploiting the new hardware features. As the scientific community looks at the end of Moore’s law, new algorithmic paradigms are needed to ensure our applications continue extracting the expected performance from the underlying hardware infrastructure. This talk highlights key algorithmic ingredients toward exascale computing in the context of computational astronomy applications, in collaboration with Paris Observatory (the European Extremely Large Telescope) and the National Astronomical Observatory of Japan (the Subaru telescope). In particular, this talk features the importance of fine-grained asynchronous computations, mixed-precision optimizations and low-rank approximations.