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Parallel Implementation of the Gauss-Seidel Algorithm on *k*-Ary *n*-Cube Machine

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In this paper, we present parallel implementation of the Gauss-Seidel (GS) iterative algorithm for the solution of linear systems of equations on a *k*-ary *n*-cube parallel machine using Open MPI as a parallel programming environment. The proposed algorithm is of *O*(*N*^{3}/*k ^{n}*) computational complexity and uses

*O*(

*nN*) communication time to decompose a matrix of order

*N*on the a

*k*-ary

*n*-cube provided

*N*≥

*k*

^{n-}^{1}. The incurred communication time is better than the best known results for hypercube,

*O*(

*N*log

*n*!), and the mesh,

*O*(

*N*

*n*!), each with approximately

*n*! nodes. The numerical results show that speedup improves as number of processors increased and the proposed algorithm has approximately 80% parallel efficiency.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

*k*-Ary

*n*-Cube Machine,"

*Applied Mathematics*, Vol. 4 No. 1A, 2013, pp. 177-182. doi: 10.4236/am.2013.41A028.

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