Accelerating Linear System Solutions Using Randomization Techniques
Accelerating Linear System Solutions Using Randomization Techniques
复制标题
使用随机化技术加速线性系统解决方案
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Tomov
中科院分区：
文献类型：
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作者：
M. Baboulin;J. Dongarra;J. Herrmann;S. Tomov
我们说明了在平方线性系统ax = b的情况下，如何通过统计技术来增强线性代数计算。与部分转换相比，这种随机性可以以非常实惠的计算价格进行，同时为我们提供了令人满意的精度。蝴蝶转化（PRBT）是根据数据存储和FLOP的计数进行了优化的。在当前的并行库中实现。
We illustrate how linear algebra calculations can be enhanced by statistical techniques in the case of a square linear system Ax = b. We study a random transformation of A that enables us to avoid pivoting and then to reduce the amount of communication. Numerical experiments show that this randomization can be performed at a very affordable computational price while providing us with a satisfying accuracy when compared to partial pivoting. This random transformation called Partial Random Butterfly Transformation (PRBT) is optimized in terms of data storage and flops count. We propose a solver where PRBT and the LU factorization with no pivoting take advantage of the current hybrid multicore/GPU machines and we compare its Gflop/s performance with a solver implemented in a current parallel library.