A blocked QR-decomposition for the parallel symmetric eigenvalue problem

In this paper we present a new stable algorithm for the parallel QR-decomposition of “tall and skinny” matrices. The algorithm has been developed for the dense symmetric eigensolver ELPA, where the QR-decomposition of tall and skinny matrices represents an important substep. Our new approach is based on the fast but unstable CholeskyQR algorithm (Stathopoulos and Wu, 2002) [1]. We show the stability of our new algorithm and provide promising results of our MPI-based implementation on a BlueGene/P and a Power6 system.