An Efficient Parallel Gauss-Seidel Algorithm on a 3D Torus Network-on-Chip

Khaled Day, Mohammad H. Al-Towaiq


Network-on-chip (NoC) multi-core architectures with a large number of processing elements are becoming a reality with the recent developments in technology. In these modern systems the processing elements are interconnected with regular NoC topologies such as meshes and tori. In this paper we propose a parallel Gauss-Seidel (GS) iterative algorithm for solving large systems of linear equations on a 3-dimensional torus NoC architecture. The proposed parallel algorithm is O(Nn2/k3) time complexity for solving a system with a matrix of order n on a k×k×k 3D torus NoC architecture with N iterations assuming n and N are large compared to k. We show that under these conditions the proposed parallel GS algorithm has near optimal speedup.




Network-on-chip; 3D torus; Parallel algorithm; Linear system of equations; Gauss-Seidel method.

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