Parallel Solution of Dense Linear Systems on the k-ary n-cube Networks

In this paper a parallel algorithm for solving systems of linear equation on the k-ary n-cube is presented and evaluated for the first time. The proposed algorithm is of O(N³/kⁿ) computation complexity and uses O(Nn) communication time to factorize a matrix of order N on the k-ary n-cube. This is better than the best known results for the hypercube, O(N log kⁿ), and the mesh, , each with approximately kⁿ nodes. The proposed parallel algorithm takes advantage of the extra connectivity in the k-ary n-cube in order to reduce the communication time involved in tasks such as pivoting, row/column interchanges, and pivot row and multipliers column broadcasts.