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