### Abstract

We present a parallel method for matrix multiplication on distributed-memory MIMD architectures based on Strassen's method. Our timing tests, performed on a 56-node Intel Paragon, demonstrate the realization of the potential of the Strassen's method with a complexity of 4.7 M^{2.807} at the system level rather than the node level at which several earlier works have been focused. The parallel efficiency is nearly perfect when the processor number is the power of 7. The parallelized Strassen's method seems always faster than the traditional matrix multiplication methods whose complexity is 2M^{3} coupled with the BMR method and the Ring method at the system level. The speed gain depends on matrix order M: 20% for M ≈ 1000 and more than 100% for M ≈ 5000.

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

Pages (from-to) | 49-69 |

Number of pages | 21 |

Journal | Computers and Mathematics with Applications |

Volume | 30 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1995 Jul |

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### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computers and Mathematics with Applications*,

*30*(2), 49-69. https://doi.org/10.1016/0898-1221(95)00077-C

}

*Computers and Mathematics with Applications*, vol. 30, no. 2, pp. 49-69. https://doi.org/10.1016/0898-1221(95)00077-C

**Parallelizing Strassen's method for matrix multiplication on distributed-memory MIMD architectures.** / Chou, C. C.; Deng, Y. F.; Li, G.; Wang, Y.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Parallelizing Strassen's method for matrix multiplication on distributed-memory MIMD architectures

AU - Chou, C. C.

AU - Deng, Y. F.

AU - Li, G.

AU - Wang, Y.

PY - 1995/7

Y1 - 1995/7

N2 - We present a parallel method for matrix multiplication on distributed-memory MIMD architectures based on Strassen's method. Our timing tests, performed on a 56-node Intel Paragon, demonstrate the realization of the potential of the Strassen's method with a complexity of 4.7 M2.807 at the system level rather than the node level at which several earlier works have been focused. The parallel efficiency is nearly perfect when the processor number is the power of 7. The parallelized Strassen's method seems always faster than the traditional matrix multiplication methods whose complexity is 2M3 coupled with the BMR method and the Ring method at the system level. The speed gain depends on matrix order M: 20% for M ≈ 1000 and more than 100% for M ≈ 5000.

AB - We present a parallel method for matrix multiplication on distributed-memory MIMD architectures based on Strassen's method. Our timing tests, performed on a 56-node Intel Paragon, demonstrate the realization of the potential of the Strassen's method with a complexity of 4.7 M2.807 at the system level rather than the node level at which several earlier works have been focused. The parallel efficiency is nearly perfect when the processor number is the power of 7. The parallelized Strassen's method seems always faster than the traditional matrix multiplication methods whose complexity is 2M3 coupled with the BMR method and the Ring method at the system level. The speed gain depends on matrix order M: 20% for M ≈ 1000 and more than 100% for M ≈ 5000.

UR - http://www.scopus.com/inward/record.url?scp=0029342667&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029342667&partnerID=8YFLogxK

U2 - 10.1016/0898-1221(95)00077-C

DO - 10.1016/0898-1221(95)00077-C

M3 - Article

AN - SCOPUS:0029342667

VL - 30

SP - 49

EP - 69

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 2

ER -