On the Efficient Parallel Computation of Legendre Transforms

In this article, we discuss a parallel implementation of efficient algorithms for computation of Legendre polynomial transforms and other orthogonal polynomial transforms. We develop an approach to the Driscoll–Healy algorithm using polynomial arithmetic and present experimental results on the accuracy, efficiency, and scalability of our implementation. The algorithms were implemented in ANSI C using the BSPlib communications library. We also present a new algorithm for computing the cosine transform of two vectors at the same time.