Parallel Solution of Dense Linear Systems on the k-ary n-cube Networks
Abdel‐Elah Al‐Ayyoub, Khaled Day · International Journal of High Speed Computing · 1997
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(N 3 /k n ) 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 k n ), and the mesh, O(N # k n ), each with approximately k n 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.