The Highly Parallel Incomplete Gram-Schmidt Preconditioner

. In this paper we study the parallel aspects of IMGS, Incomplete Modified Gram-Schmidt preconditioner which can be used for efficiently solving sparse and large linear systems and least squares problems on massively parallel distributed memory computers. The performance of this preconditioning technique on this kind of architecture is always limited because of the global communication required for the inner products, even for ParIMGS, a parallel version of IMGS where we create some possibilities such that the computation can be overlapped with the communication. We will describe a more efficient alternative, namely Improved ParIMGS (IParIMGS) which avoids the global communication of inner products and only requires local communications. Therefore, the cost of communication can be significantly reduced. Several numerical experiments carried out on Parsytec GC/PowerPlus are presented as well. 1 Introduction Preconditioning techniques that accelerate the convergence of the ..