Parallel divide-and-Conquer algorithm for solving tridiagonal eigenvalue problems on manycore systems

Abstract

We present a new parallel divide-and-conquer (DC) algorithm based on an execution scheduling by batched kernels for solving real-symmetric tridiagonal eigenvalue problems on manycore systems. Our algorithm has higher parallelism and requires less global synchronizations than a conventional algorithm. We compared the performance of the solver based on our algorithm with that of Intel MKL’s DC solver and PLASMA’s one on Xeon E5, Xeon Phi Knights Corner, and Xeon Phi Knights Landing. The numerical tests show that the implementation of our algorithm is comparable to Intel MKL on Xeon E5 and outperforms Intel MKL and PLASMA on the two Xeon Phi systems.