### Abstract

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) commun ication time to factorize a matrix of order N on the k-airy 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.

Original language | English |
---|---|

Pages (from-to) | 85-99 |

Number of pages | 15 |

Journal | International Journal of High Speed Computing |

Volume | 9 |

Issue number | 2 |

Publication status | Published - Jun 1997 |

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### Keywords

- Interconnection topologies
- k-ary n-cube
- Linear systems
- Parallel computing

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Theoretical Computer Science

### Cite this

*International Journal of High Speed Computing*,

*9*(2), 85-99.

**Parallel solution of systems on the k-ary n-cube networks.** / Al-Ayyoub, Abdel Elah; Day, Khaled.

Research output: Contribution to journal › Article

*International Journal of High Speed Computing*, vol. 9, no. 2, pp. 85-99.

}

TY - JOUR

T1 - Parallel solution of systems on the k-ary n-cube networks

AU - Al-Ayyoub, Abdel Elah

AU - Day, Khaled

PY - 1997/6

Y1 - 1997/6

N2 - 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) commun ication time to factorize a matrix of order N on the k-airy n-cube. This is better than the best known results for the hypercube, O(N log kn), and the mesh, O(N√kn), 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.

AB - 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) commun ication time to factorize a matrix of order N on the k-airy n-cube. This is better than the best known results for the hypercube, O(N log kn), and the mesh, O(N√kn), 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.

KW - Interconnection topologies

KW - k-ary n-cube

KW - Linear systems

KW - Parallel computing

UR - http://www.scopus.com/inward/record.url?scp=0006192445&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0006192445&partnerID=8YFLogxK

M3 - Article

VL - 9

SP - 85

EP - 99

JO - International Journal of High Speed Computing

JF - International Journal of High Speed Computing

SN - 0129-0533

IS - 2

ER -