Randomized LU Decomposition Using Sparse Projections

TL;DR

This paper introduces a fast, parallelizable algorithm for low-rank LU decomposition using sparse and FFT-based random projections, offering improved speed and efficiency over existing methods.

Contribution

It presents a novel low-complexity LU approximation algorithm combining sparse and FFT-based projections with theoretical error bounds.

Findings

The sparse LU algorithm is faster than recent methods for similar accuracy.

The algorithm is fully parallelizable and optimized for GPU execution.

Numerical tests confirm significant speed improvements on GPU.

Abstract

A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation error of the algorithm is analyzed and a theoretical error bound is presented. Finally, numerical examples illustrate that for a similar approximation error, the sparse LU algorithm is faster than recent state-of-the-art methods. The algorithm is completely parallelizable that enables to run on a GPU. The performance is tested on a GPU card, showing a significant improvement in the running time in comparison to sequential execution.