计算机工程

• 先进计算与数据处理 • 上一篇    下一篇

基于GPGPU的大整数矩阵行列式快速准确计算方法

魏渐俊,陈良育   

  1. (华东师范大学 上海高可信计算重点实验室,上海 200062)
  • 收稿日期:2017-01-20 出版日期:2018-03-15 发布日期:2018-03-15
  • 作者简介:魏渐俊(1992—),男,硕士研究生,主研方向为大规模科学计算;陈良育,副教授。
  • 基金项目:
    国家自然科学基金(11471209);中央高校基本科研业务费专项资金(78210152)。

Fast and Accurate Determinant Calculation Method for Large Integer Matrix Based on GPGPU

WEI Jianjun,CHEN Liangyu   

  1. (Shanghai Key Lab of Trustworthy Computing,East China Normal University,Shanghai 200062,China)
  • Received:2017-01-20 Online:2018-03-15 Published:2018-03-15

摘要: 传统计算数值矩阵行列式的方法多数基于串行计算,存在初等变换频繁、计算缓慢等问题。为此,提出基于通用计算图形处理器(GPGPU)的计算方法,以快速准确解决大整数矩阵行列式计算问题。在众核环境下利用GPGPU和模方法并行求解整数矩阵行列式,以加速计算过程并避免浮点运算误差,同时运用中国剩余定理得到准确计算结果。实验结果表明,与常用Maple、NTL等计算软件相比,该方法计算速度快,消耗内存少,可解决计算过程中内存膨胀的问题,对于高阶整数矩阵行列式优势较为明显。

关键词: 通用计算图形处理器, 行列式, 高性能计算, 并行算法, 模方法

Abstract: In the conventional serial calculation method,there are some problems such as frequent elementary transformation in the solution method and large-scale calculation of high-order numerical determinants.Therefore,a fast and accurate calculation method of determinant based on General Purpose Graphic Process Units(GPGPU) is proposed.Using GPGPU and modular methods to solve integer matrix determinants in parallel in all nuclear environments,the calculation process can be accelerated to avoid floating point errors and the Chinese residual theorem can be used to obtain accurate results.Experimental results show that compared with the commonly used calculation software such as Maple and NTL,this method has the advantages of high computational speed,less memory consumption and memory expansion during calculation,which is more obvious for the higher-order integer matrix determinant.

Key words: General Purpose Graphic Process Units(GPGPU), determination, high performance computing, parallel algorithm, modular method

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