Batched QR and SVD Algorithms on GPUs with Applications in Hierarchical Matrix Compression.

•High performance GPU hosted batched QR decomposition kernels are developed and outperform current implementations for small and rectangular matrices.•Various GPU hosted batched singular value decomposition kernels are developed and used as building blocks of a batched randomized SVD kernel for numerically low rank matrix blocks.•Batched QR, SVD, and GEMM kernels are used to compress hierarchical matrices entirely on the GPU.