GPU Acceleration of Newton's Method for Large Systems of Polynomial Equations in Double Double and Quad Double Arithmetic
GPU Acceleration of Newton's Method for Large Systems of Polynomial Equations in Double Double and Quad Double Arithmetic
复制标题
双双和四双算术大型多项式方程组牛顿法的 GPU 加速
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Xiangcheng Yu
中科院分区：
文献类型：
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作者：
J. Verschelde;Xiangcheng Yu
为了弥补双倍和四倍运算在求解大型多项式系统时的较高成本，我们研究了NVIDIA Tesla K20C图形处理单元（GPU）的应用。本文的重点是牛顿的方法，它需要评估的多项式，其衍生物，并解决一个线性系统计算更新到当前的近似解决方案。变量乘积的算法微分的反向模式以二叉树的方式重写，因此块中的所有线程可以在计算中协作。对于二重运算，求值和微分问题是内存限制，而对于复杂的四重运算，问题是计算限制。通过加速，我们可以将维度加倍，并在大约相同的时间内获得两倍准确的结果。
In order to compensate for the higher cost of double double and quad double arithmetic when solving large polynomial systems, we investigate the application of the NVIDIA Tesla K20C graphics processing unit (GPU). The focus on this paper is on Newton's method, which requires the evaluation of the polynomials, their derivatives, and the solution of a linear system to compute the update to the current approximation for the solution. The reverse mode of algorithmic differentiation for a product of variables is rewritten in a binary tree fashion so all threads in a block can collaborate in the computation. For double arithmetic, the evaluation and differentiation problem is memory bound, whereas for complex quad double arithmetic the problem is compute bound. With acceleration we can double the dimension and get results that are twice as accurate in about the same time.
使用 ADOL-C 的 OpenMP 程序的并行反向模式自动微分
DOI：
10.1007/978-3-540-68942-3_15
发表时间：
2008
期刊：
影响因子：
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作者：
C. Bischof;N. Guertler;A. Kowarz;A. Walther:
通讯作者：
A. Walther: