Optimal algorithms for parallel polynomial evaluation

Optimal Algorithms for Parallel Polynomial Evaluation

Stability of Parallel Algorithms for Polynomial Evaluation

In this paper, we analyse the stability of parallel algorithms for the evaluation of polynomials written es a finite series of orthogonal polynomials. The basic part of the computation is the solution of a triangular tridiagonal linear system. This fact allows us to present a more detailed analysis. The theoretical results show that the parallel algorithms are almost as stable as their sequenti...

Optimal Parallel Randomized Algorithms for . . .

Optimal and Nearly Optimal Algorithms for Approximating Polynomial Zeros

K e y w o r d s C o m p l e x polynomial zeros, Approximation, Polynomial factorization, Parallel algorithms, Computational complexity, Sequential algorithms. 1. I N T R O D U C T I O N 1.1. T h e Subject , Some History, and a S u m m a r y of Our Resul ts The problem of solving a polynomial equation p ( x ) = 0 substantially motivated the development of mathematics throughout the centuries. As...

Optimal Parallel Hypercube Algorithms for Polygon Problems

We present parallel techniques on hypercubes for solving optimally a class of polygon problems. We thus obtain optimal O(logn)-lime, n-processor hypercube algorithms for the problems of computing the portions of an n-vertex simple polygonal chain C that are visible from a given source point, computing the convex hull of C, testing an n-verlex simple polygon P for monotonicity, and other related...