Parallel algorithms for some algebraic operations on polynomial equations

Abstract

We give a group of parallel methods for solving polynomial related problems and their implementation on a distributed memory multicomputer. These problems are 1. the evaluation of polynomials, 2. the multiplication of polynomials, 3. the division of polynomials, and 4. the interpolation of polynomials. Mathematical analyses are given for exploiting the parallelism of these operations. The related parallel methods supporting the solutions of these polynomial problems, such as FFT, Toeplitz linear systems and others are also discussed.