在GPU计算处理器上评估多元多项式及其导数
Evaluating polynomials in several variables and their derivatives on a GPU computing processor
AI总结：
本文利用多精度算术和GPU加速，提出并实现了稀疏多元多项式的大规模并行评估与算法微分方法，以提高数值延续法求解多项式系统的精度。
摘要：
为了通过数值延续法获得多项式系统更精确的解，我们使用多精度算术。我们的目标是利用通用图形处理单元加速路径跟踪器，特别是牛顿法，以抵消双倍双精度算术的开销。在本文中，我们描述了用于大规模并行评估和微分多个变量中稀疏多项式的算法。我们报告了在NVIDIA Tesla C2050计算处理器上使用NVIDIA CUDA编译器工具实现变量乘积的算法微分的情况。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
