The advent of multicore processors and other technologies like Graphical Processing Units (GPU) will considerably influence future research in High Performance Computing.
To take advantage of these architectures in dense linear algebra operations, new algorithms are proposed that use finer granularity and minimize synchronization points.
After presenting some of these algorithms, we address the issue of pivoting and investigate randomization techniques to avoid pivoting in some cases.
In the particular case of GPUs, we show how linear algebra operations can be enhanced using hybrid CPU-GPU calculations and mixed precision algorithms.
