2017/07/13 by Wajih Boukaram, George Turkiyyah, Boukaram, Wajih Halim +5
Computer Science · Engineering · Mathematics · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1707.05141
openalex publication_date 2017/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present high performance implementations of the QR and the singular value\ndecomposition of a batch of small matrices hosted on the GPU with applications\nin the compression of hierarchical matrices. The one-sided Jacobi algorithm is\nused for its simplicity and inherent parallelism as a building block for the\nSVD of low rank blocks using randomized methods. We implement multiple kernels\nbased on the level of the GPU memory hierarchy in which the matrices can reside\nand show substantial speedups against streamed cuSOLVER SVDs. The resulting\nbatched routine is a key component of hierarchical matrix compression, opening\nup opportunities to perform H-matrix arithmetic efficiently on GPUs.\n