Evaluating Polynomials in Several Variables and their Derivatives on a GPU Computing Processor

Author

Verschelde, Jan ; Yoffe, Genady

Author_Institution

Dept. of Math., Stat., & Comput. Sci., Univ. of Illinois at Chicago, Chicago, IL, USA

fYear

2012

fDate

21-25 May 2012

Firstpage

1397

Lastpage

1405

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.

Keywords

Newton method; differentiation; digital arithmetic; graphics processing units; parallel architectures; polynomials; program compilers; GPU computing processor; NVIDIA CUDA compiler tools; NVIDIA Tesla C2050 computing processor; Newton method; double double arithmetic; general purpose graphics processing unit; multiprecision arithmetic; numerical continuation methods; path trackers; polynomial evaluation; polynomial systems; sparse polynomials differentiation; Arrays; Encoding; Graphics processing unit; Instruction sets; Jacobian matrices; Kernel; Polynomials; Speelpenning product; algoritmic differentiation; compute unified device architecture (CUDA); graphics processing unit (GPU); massively parallel polynomial evaluation;

fLanguage

English

Publisher

ieee

Conference_Titel

Parallel and Distributed Processing Symposium Workshops & PhD Forum (IPDPSW), 2012 IEEE 26th International

Conference_Location

Shanghai

Print_ISBN

978-1-4673-0974-5

Type

conf

DOI

10.1109/IPDPSW.2012.177

Filename

6270807