Minimizing communication overhead for matrix inversion algorithms on hypercubes

Abstract

We propose novel parallel Gauss-Jordan inversion algorithms (with or without partial pivoting) under different data partitioning strategies. The machine model we assume is a MIMD hypercube, using asynchronous message passing, with the software supporting user specified interrupt handling. These algorithms achieve almost optimal overlapping of communication delays by computation, leading to a minimization of communication overhead. Furthermore, it is shown that the optimal data layout for our algorithms is different from that for hypercubes that do not overlap communication and computation. Rigorous analytical and numerical performance analysis of our parallel algorithms are presented as well. >