Efficient Gaussian Elimination on a 2D SIMD Array of Processors without Column Broadcasts

TL;DR

This paper introduces an optimized Gaussian elimination algorithm for a 2D SIMD processor array that reduces communication overhead by eliminating the need for column broadcasts, achieving optimal speed-up.

Contribution

The paper proposes a novel Gaussian elimination method tailored for 2D SIMD arrays that minimizes broadcasts and improves efficiency over traditional serial approaches.

Findings

Algorithm completes in O(n) iterations

Achieves optimal speed-up over serial implementation

Requires only row broadcasts, not column broadcasts

Abstract

This paper presents an efficient method for implementing the Gaussian elimination technique for an nxm (m>=n) matrix, using a 2D SIMD array of nxm processors. The described algorithm consists of 2xn-1=O(n) iterations, which provides an optimal speed-up over the serial version. A particularity of the algorithm is that it only requires broadcasts on the rows of the processor matrix and not on its columns. The paper also presents several extensions and applications of the Gaussian elimination algorithm.