Stability of parallel algorithms for 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 Algorithms for Parallel Polynomial Evaluation

A Unified Approach for Design of Lp Polynomial Algorithms

By summarizing Khachiyan's algorithm and Karmarkar's algorithm forlinear program (LP) a unified methodology for the design of polynomial-time algorithms for LP is presented in this paper. A key concept is the so-called extended binary search (EBS) algorithm introduced by the author. It is used as a unified model to analyze the complexities of the existing modem LP algorithms and possibly, help ...

Parallel Homotopy Algorithms to Solve Polynomial Systems

Homotopy continuation methods to compute numerical approximations to all isolated solutions of a polynomial system are known as “embarrassingly parallel”, i.e.: because of their low communication overhead, these methods scale very well for a large number of processors. Because so many important problems remain unsolved mainly due to their intrinsic computational complexity, it would be embarras...

FPGA Implementation of Polynomial Evaluation Algorithms

The most-significant-digit-first function evaluation method (E-method) allows efficient evaluation of polynomials and certain rational functions on custom hardware. The time required for the computation is of the order of m carry-free addition operations, m being the number of digits in the result. We discuss a digit-parallel and a digit-serial implementation of this method on a DecPeRLe-1 boar...