Evaluating polynomials in several variables and their derivatives on a GPU computing processor

TL;DR

This paper presents algorithms and implementation for efficiently evaluating and differentiating sparse multivariable polynomials on GPUs, aiming to improve numerical solutions of polynomial systems with multiprecision arithmetic.

Contribution

It introduces parallel algorithms for polynomial evaluation and differentiation on GPUs, specifically leveraging CUDA for sparse multivariable polynomials with multiprecision arithmetic.

Findings

Achieved accelerated polynomial evaluation and differentiation on GPU

Implemented algorithms for sparse multivariable polynomials

Demonstrated performance improvements on NVIDIA Tesla C2050

Abstract

In order to obtain more accurate solutions of polynomial systems with numerical continuation methods we use multiprecision arithmetic. Our goal is to offset the overhead of double double arithmetic accelerating the path trackers and in particular Newton's method with a general purpose graphics processing unit. In this paper we describe algorithms for the massively parallel evaluation and differentiation of sparse polynomials in several variables. We report on our implementation of the algorithmic differentiation of products of variables on the NVIDIA Tesla C2050 Computing Processor using the NVIDIA CUDA compiler tools.