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

TL;DR

This paper develops high-performance GPU algorithms for batched QR and SVD computations, enabling efficient hierarchical matrix compression with significant speedups over existing methods.

Contribution

It introduces GPU-optimized batched QR and SVD algorithms using the Jacobi method and randomized techniques, tailored for hierarchical matrix applications.

Findings

Substantial speedups over cuSOLVER SVDs achieved

Effective GPU kernels based on memory hierarchy levels implemented

Enables efficient H-matrix arithmetic on GPUs

Abstract

We present high performance implementations of the QR and the singular value decomposition of a batch of small matrices hosted on the GPU with applications in the compression of hierarchical matrices. The one-sided Jacobi algorithm is used for its simplicity and inherent parallelism as a building block for the SVD of low rank blocks using randomized methods. We implement multiple kernels based on the level of the GPU memory hierarchy in which the matrices can reside and show substantial speedups against streamed cuSOLVER SVDs. The resulting batched routine is a key component of hierarchical matrix compression, opening up opportunities to perform H-matrix arithmetic efficiently on GPUs.