Solution of eigenvalue problems on heterogeneous computing architectures

In this paper are presented current achievements and the state-of-the-art algorithms and implementations for dense linear algebra on traditional architectures such as single-core machines or distributed memory parallel machines. Also, this paper summarizes the current implementations and publicly available libraries for basic linear algebra for multi-core and many-core architectures (e.g. graphic processors), but also emphasizes the lack of advanced linear algebra implementation on the multiand many-core architectures. The problem that will be solved during this research is to speed-up the execution of the decomposition phase (i.e. Hessenberg reduction, tridiagonalization, bidiagonalization) for the symmetric eigenvalue problem by utilizing the heterogeneous architectures (CPU + GPU). The final aim of this research is to explore the use of external devices, in particular, general purpose GPUs (GPGPUs), to accelerate the solution of matrix eigenvalue problems. Also, interesting topic will be to explore the applicability of the implementation results for symmetric eigenvalue problem to the SVD decomposition on the multiand many-core architectures.