Communication-Avoiding Tile QR Decomposition on CPU/GPU Heterogeneous Cluster System

The tile algorithm for matrix decompositions is attracting attention as a method for the latest multicore/many-core architecture because it can generate many fine-grained tasks which can be executed in parallel. Exploiting many parallel computing resources effectively with a fork-join paradigm is difficult. CPU/GPU heterogeneous cluster system is mainstream for a supercomputer system in recent years. Using the CPU/GPU cluster system efficiently is more difficult than efficiently utilizing the multicore cluster system. We implemented the tile CAQR decomposition algorithm on the CPU/GPU cluster system with OpenMP 4.0, MPI and cuBLAS, and proposed new approaches to utilize GPUs efficiently. In this paper, we show the performance result of our implementation on the Reedbush-H heterogeneous supercomputer.