Scheduling Two-sided Transformations using Algorithms-by-Tiles on Multicore Architectures LAPACK Working Note # 214

The objective of this paper is to describe, in the context of multicore architectures, different scheduler implementations for the two-sided linear algebra transformations, in particular the Hessenberg and Bidiagonal reductions which are the first steps for the standard eigenvalue problems and the singular value decompositions respectively. State-of-the-art dense linear algebra softwares, such as the LAPACK and ScaLAPACK libraries, suffer performance losses on multicore processors due to their inability to fully exploit thread-level parallelism. At the same time the coarse-grain dataflow model gains popularity as a paradigm for programming multicore architectures. By using the concepts of algorithms-by-tiles [Buttari et al., 2007] along with efficient mechanisms for data-driven execution, these two-sided reductions achieve high performance computing. The main drawback of the algorithms-bytiles approach for two-sided transformations is that the full reduction can not be obtained in one stage. Other methods have to be considered to further reduce the band matrices to the required forms.