A parallel algorithm for lagrange interpolation on k-ary n-cubes

Hamid Sarbazi-Azad; Lewis M. Mackenzie; Mohamed Ould-Khaoua

doi:10.1007/3-540-49164-3_9

A parallel algorithm for lagrange interpolation on k-ary n-cubes

Hamid Sarbazi-Azad, Lewis M. Mackenzie, Mohamed Ould-Khaoua

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

4 Citations (Scopus)

Abstract

Most current multicomputers employ k- ary n-cube networks for lowlatency and high-bandwidth inter-processor communication. This paper introduces a parallel algorithm for computing an N=kⁿ point Lagrange interpolation on these networks. The algorithm consists of three phases: initialisation, main and final. While there is no computation in the initialisation phase, the main phase is composed of kⁿ/2 steps, each consisting of four multiplications and four subtractions, and an additional step including one division and one multiplication. The final phase is carried out in n×⌈k/2⌉ steps, each using one addition.

Original language	English
Title of host publication	Parallel Computation - 4th International ACPC Conference Including Special Tracks on Parallel Numerics (ParNum 1999) and Parallel Computing in Image Processing, Video Processing, and Multimedia, Proceedings
Editors	Peter Zinterhof, Marian Vajteršic, Andreas Uhl
Publisher	Springer Verlag
Pages	85-95
Number of pages	11
ISBN (Print)	3540656413, 9783540656418
DOIs	https://doi.org/10.1007/3-540-49164-3_9
Publication status	Published - 1999
Externally published	Yes
Event	4th International ACPC Conference on Parallel Computation, ACPC 1999 - Salzburg, Austria Duration: Feb 16 1999 → Feb 18 1999

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1557
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	4th International ACPC Conference on Parallel Computation, ACPC 1999
Country/Territory	Austria
City	Salzburg
Period	2/16/99 → 2/18/99

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-49164-3_9

Cite this

Sarbazi-Azad, H., Mackenzie, L. M., & Ould-Khaoua, M. (1999). A parallel algorithm for lagrange interpolation on k-ary n-cubes. In P. Zinterhof, M. Vajteršic, & A. Uhl (Eds.), Parallel Computation - 4th International ACPC Conference Including Special Tracks on Parallel Numerics (ParNum 1999) and Parallel Computing in Image Processing, Video Processing, and Multimedia, Proceedings (pp. 85-95). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1557). Springer Verlag. https://doi.org/10.1007/3-540-49164-3_9

A parallel algorithm for lagrange interpolation on k-ary n-cubes. / Sarbazi-Azad, Hamid; Mackenzie, Lewis M.; Ould-Khaoua, Mohamed.
Parallel Computation - 4th International ACPC Conference Including Special Tracks on Parallel Numerics (ParNum 1999) and Parallel Computing in Image Processing, Video Processing, and Multimedia, Proceedings. ed. / Peter Zinterhof; Marian Vajteršic; Andreas Uhl. Springer Verlag, 1999. p. 85-95 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1557).

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

Sarbazi-Azad, H, Mackenzie, LM & Ould-Khaoua, M 1999, A parallel algorithm for lagrange interpolation on k-ary n-cubes. in P Zinterhof, M Vajteršic & A Uhl (eds), Parallel Computation - 4th International ACPC Conference Including Special Tracks on Parallel Numerics (ParNum 1999) and Parallel Computing in Image Processing, Video Processing, and Multimedia, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1557, Springer Verlag, pp. 85-95, 4th International ACPC Conference on Parallel Computation, ACPC 1999, Salzburg, Austria, 2/16/99. https://doi.org/10.1007/3-540-49164-3_9

Sarbazi-Azad H, Mackenzie LM, Ould-Khaoua M. A parallel algorithm for lagrange interpolation on k-ary n-cubes. In Zinterhof P, Vajteršic M, Uhl A, editors, Parallel Computation - 4th International ACPC Conference Including Special Tracks on Parallel Numerics (ParNum 1999) and Parallel Computing in Image Processing, Video Processing, and Multimedia, Proceedings. Springer Verlag. 1999. p. 85-95. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-49164-3_9

Sarbazi-Azad, Hamid ; Mackenzie, Lewis M. ; Ould-Khaoua, Mohamed. / A parallel algorithm for lagrange interpolation on k-ary n-cubes. Parallel Computation - 4th International ACPC Conference Including Special Tracks on Parallel Numerics (ParNum 1999) and Parallel Computing in Image Processing, Video Processing, and Multimedia, Proceedings. editor / Peter Zinterhof ; Marian Vajteršic ; Andreas Uhl. Springer Verlag, 1999. pp. 85-95 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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A parallel algorithm for lagrange interpolation on k-ary n-cubes

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