Diamond matrix powers kernels

Matrix powers kernel calculates the vectors Akv, for k = 1, 2,..., m and they are the heart of various scientific computations, including communication avoiding iterative solvers. In this paper we propose diamond matrix powers kernel - DMPK, which has the purpose to apply the "diamond tiling" stencil algorithm to general matrices. It can also be considered as an extension of the PA1 and PA2 algorithms, introduced by Demmel et al. Our approach enables us to control the balance between the amount of communication avoidance and redundant computation inherently present in communication avoiding algorithms. We present a proof of concept implementation of the algorithm using MPI routines. The experiments we performed show that the control of the amount of computation and communication is achievable, and with more thorough optimisations, DMPK is a promising alternative to existing MPK approaches.