Efficient Parallel Blocked Algorithms for Generalized Hermitian Eigenproblem

The performance of a generalized eigenproblem solver relies on many factors, which include selected parallel algorithms and matrix mapping strategy. A new parallelization is presented, which combines the Cholesky into the transformation from generalized to standard form. By reducing the communication cost and extending the parallelism, the new algorithm can obviously improve the performance and scalability of the original algorithm. Moreover, an efficient parallel algorithm is proposed to compute a triangular AX=B with multiple right hand sides. From the tests using the parallel software PSEPS, the speed of the parallel algorithm is about two times that of the classical parallel algorithms, and it has better performance and scalability than the classical parallel algorithms.