Implementing the matrix inversion by Gauss-Jordan method with CUDA

Abstract

Solving the matrix inversion is an open problem which is often related to scientific computation. Moreover, matrix inverse also has wide applications in social networks. Individuals in social networks are described as nodes, and the similarity among nodes are significant for link prediction. Usually, the problem of calculating similarities among nodes is converted to the problem of matrix inversion. With the increasing of the orders of matrices, traditional sequential algorithms are unable to meet the needs for the short calculation time. Although cluster systems can solve the inversion of large-scale matrices efficiently, the equipment cost and power consumption are very high. This paper proposes a parallel algorithm PA-Gauss, which is based on the Gauss-Jordan method of selecting the main element. CUDA (Computer Unified Device Architecture) of GPU (Graphic Process Unit) is used to implement the proposed algorithm to solve inversions of the real and complex matrices. The experimental results show that the Gauss-Jordan algorithm can save more running time than traditional sequential algorithms and the speedup ratio of PA-Gauss for Real Matrices is 633~100435, and the speedup ratio of PA-Gauss for Complex Matrices is 224~36508. Therefore,the computing time of solving the matrix inversions is reduced significantly.