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

2012/01/02 by Jan Verschelde, Verschelde, Jan, Genady Yoffe +1
Computer Science · #Cryptography and Residue Arithmetic #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1201.0499

openalex publication_date 2012/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Quality Up in Polynomial Homotopy Continuation by Multithreaded Path Tracking

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