Using graphics processors to accelerate the computation of the matrix inverse

Abstract

We study the use of massively parallel architectures for computing a matrix inverse. Two different algorithms are reviewed, the traditional approach based on Gaussian elimination and the Gauss-Jordan elimination alternative, and several high performance implementations are presented and evaluated. The target architecture is a current general-purpose multi-core processor (CPU) connected to a graphics processor (GPU). Numerical experiments show the efficiency attained by the proposed implementations and how the computation of large-scale inverses, which only a few years ago would have required a distributed-memory cluster, take only a few minutes on a hybrid architecture formed by a multi-core CPU and a GPU.