A Parallel Algorithm for Lagrange Interpolation on k-ary n-Cubes

Authors:
Hamid Sarbazi-Azad;Lewis M. Mackenzie;Mohamed Ould-Khaoua
Affiliations:
-;-;-
Venue:
ParNum '99 Proceedings of the 4th International ACPC Conference Including Special Tracks on Parallel Numerics and Parallel Computing in Image Processing, Video Processing, and Multimedia: Parallel Computation
Year:
1999

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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.