An efficient implementation of parallel eigenvalue computation for massively parallel processing

A Massively Parallel Dense Symmetric Eigensolver with Communication Splitting Multicasting Algorithm

“…For the parallel algorithm for a square grid [4], that is, the case of p=q, tridiagonalization is used, as described in Figure 3.…”

“…The Case of a Rectangle Grid (p < q) In [4], there is no description of rectangle process grid algorithms for the rectangle grid (p < q). However, the algorithm can be constructed by exchanging MPI_BCAST in Figure 3 with MPI_ALLREDUCE.…”

“…Katagiri et al [4] proposed a massively parallel algorithm with a communication splitting multicast algorithm. The algorithm established more than a 5x speedup compared to that of ScaLAPACK [4], although the algorithm does not implement a blocking algorithm.…”

“…The algorithm established more than a 5x speedup compared to that of ScaLAPACK [4], although the algorithm does not implement a blocking algorithm. The drawback of this algorithm was the restriction of process grid construction.…”

“…First, we propose a process grid free algorithm based on [4]. This enables us not only many opportunities to adapt our algorithm, but also another tuning approach.…”