Abstract
This chapter introduces innovative approaches for the efficient use of some of the most novel techniques based on tasking to optimize dense linear algebra operations. The idea is to explore high-level programming techniques that increment the programming productivity and performance for dense linear algebra operations. The authors apply these techniques on some of the most important and widely used dense linear algebra kernels, such as the GEMM and TRSM routines of the BLAS-3 standard, as well as the LU factorization and solve of the LAPACK library. The authors use as target platforms two different current HPC architectures: a CPU multi-core processor and a GPU hardware accelerator. Different approaches are presented depending on the target platform, but always based on tasking.