论文标题
在GPU上优化的多元多项式决定因素
Optimized Multivariate Polynomial Determinant on GPU
论文作者
论文摘要
我们提出了一种优化的算法，该算法计算了GPU上多元多项式基质的决定归因。新型算法在可控时间内为输入多元多项式基质提供了精确的决定因素。我们的方法基于模块化方法，分为快速的傅立叶变换，冷凝法和中文定理，其中每种算法在GPU上平行。实验结果表明，与枫木相比，我们的并行方法具有大量加速，从而使内存开销和时间探险以稳定的增量。我们还能够处理超过枫树上阈值并在CPU上限制的复杂矩阵。此外，无论遇到什么干扰，都可以在不失去准确性的情况下恢复过程中的计算。此外，我们根据某些基本矩阵属性提出了计算多项式决定因素的时间预测，并根据我们的GPU实现解决了与谐波消除方程相关的开放问题。
We present an optimized algorithm calculating determinant for multivariate polynomial matrix on GPU. The novel algorithm provides precise determinant for input multivariate polynomial matrix in controllable time. Our approach is based on modular methods and split into Fast Fourier Transformation, Condensation method and Chinese Remainder Theorem where each algorithm is paralleled on GPU. The experiment results show that our parallel method owns substantial speedups compared to Maple, allowing memory overhead and time expedition in steady increment. We are also able to deal with complex matrix which is over the threshold on Maple and constrained on CPU. In addition, calculation during the process could be recovered without losing accuracy at any point regardless of disruptions. Furthermore, we propose a time prediction for calculation of polynomial determinant according to some basic matrix attributes and we solve an open problem relating to harmonic elimination equations on the basis of our GPU implementation.
