QR Factorization of Block Low-Rank Matrices on Multi-instance GPU

The QR factorization, which is a fundamental operation in linear algebra, is used extensively in scientific simulations. The acceleration and memory reduction of it are important research targets. QR factorization using block low-rank matrices (BLR-QR) has previously been proposed to address this issue. In this study, we consider its implementation on a GPU. Current CPUs and GPUs have numerous computational cores and the performance consists of the total performance of them. Therefore, the degree of parallelism of the target calculation is important for obtaining high performance. By contrast, many applications, including BLR-QR, do not have sufficient parallelism. Batched computation has attracted attention for achieving high performance in such calculations. However, the use of it requires major code rewriting and is extremely laborious. Thus, we propose the use of the multi-instance GPU (MIG) feature of current GPUs. Using MIG, we succeeded in obtaining a 53.3% time reduction over the CPU and 77.6% over the GPU without MIG. From the above result, we succeeded in demonstrating rapid implementation of BLR-QR on MIG and usefulness of MIG.