A novel parallel algorithm for Gaussian Elimination of sparse unsymmetric matrices

TL;DR

This paper introduces a new parallel algorithm for Gaussian Elimination tailored for sparse, unsymmetric matrices, offering scalable performance and a practical MPI implementation for rank computation.

Contribution

The paper presents a novel parallel Gaussian Elimination algorithm for sparse matrices, with a distributed-memory formulation and preliminary performance evaluation.

Findings

Algorithm degrades gracefully to sequential execution

MPI implementation successfully computes matrix rank

Preliminary results compare favorably with existing algorithms

Abstract

We describe a new algorithm for Gaussian Elimination suitable for general (unsymmetric and possibly singular) sparse matrices, of any entry type, which has a natural parallel and distributed-memory formulation but degrades gracefully to sequential execution. We present a sample MPI implementation of a program computing the rank of a sparse integer matrix using the proposed algorithm. Some preliminary performance measurements are presented and discussed, and the performance of the algorithm is compared to corresponding state-of-the-art algorithms for floating-point and integer matrices.