### Abstract

This paper introduces a parallel algorithm for computing an N = n!-point Lagrange interpolation on an n-star (n>2). It exploits several communication techniques on stars in a novel way which can be adapted for computing similar functions. The algorithm is optimal and consists of three phases: initialization, main and final. While there is no computation in the initialization phase, the main phase is composed of n!/2 steps, each consisting of four multiplications, four subtractions and one communication operation, and an additional step including one division and one multiplication. The final phase is carried out in (n-1) sub-phases each with O(log n) steps where each step takes three communications and one addition.

Original language | English |
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Title of host publication | Proceedings of the International Parallel Processing Symposium, IPPS |

Publisher | IEEE |

Pages | 777-782 |

Number of pages | 6 |

Publication status | Published - 2000 |

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### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Proceedings of the International Parallel Processing Symposium, IPPS*(pp. 777-782). IEEE.

**Parallel Lagrange interpolation on the star graph.** / Sarbazi-Azad, H.; Ould-Khaoua, M.; Mackenzie, L. M.; Akl, S. G.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Proceedings of the International Parallel Processing Symposium, IPPS.*IEEE, pp. 777-782.

}

TY - CHAP

T1 - Parallel Lagrange interpolation on the star graph

AU - Sarbazi-Azad, H.

AU - Ould-Khaoua, M.

AU - Mackenzie, L. M.

AU - Akl, S. G.

PY - 2000

Y1 - 2000

N2 - This paper introduces a parallel algorithm for computing an N = n!-point Lagrange interpolation on an n-star (n>2). It exploits several communication techniques on stars in a novel way which can be adapted for computing similar functions. The algorithm is optimal and consists of three phases: initialization, main and final. While there is no computation in the initialization phase, the main phase is composed of n!/2 steps, each consisting of four multiplications, four subtractions and one communication operation, and an additional step including one division and one multiplication. The final phase is carried out in (n-1) sub-phases each with O(log n) steps where each step takes three communications and one addition.

AB - This paper introduces a parallel algorithm for computing an N = n!-point Lagrange interpolation on an n-star (n>2). It exploits several communication techniques on stars in a novel way which can be adapted for computing similar functions. The algorithm is optimal and consists of three phases: initialization, main and final. While there is no computation in the initialization phase, the main phase is composed of n!/2 steps, each consisting of four multiplications, four subtractions and one communication operation, and an additional step including one division and one multiplication. The final phase is carried out in (n-1) sub-phases each with O(log n) steps where each step takes three communications and one addition.

UR - http://www.scopus.com/inward/record.url?scp=0033894866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033894866&partnerID=8YFLogxK

M3 - Chapter

SP - 777

EP - 782

BT - Proceedings of the International Parallel Processing Symposium, IPPS

PB - IEEE

ER -