论文标题
混合精度矩阵插值分解用于模型还原
Mixed precision matrix interpolative decompositions for model reduction
论文作者
论文摘要
由于数据容量和带宽的不断增长以及GPU的进步，对混合精液算法的新兴趣已经出现，这使得低精度算术能够显着加速。鉴于此，我们提出了一种混合精确算法来生成在给定的标准下的双精度精确矩阵插值分解近似。尽管较低的精度算术遭受了更快的圆形误差积累，但是对于许多数据丰富的应用程序，我们仍然达到可行的近似准确性，因为使用低精度算术算法所产生的误差以低级别近似固有的误差为主。然后，我们进行了几项模拟数值测试，以证明算法的疗效和相应的误差估计值。最后，我们介绍了算法在含粒子湍流的模型降低中的应用。
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose a mixed-precision algorithm to generate a double-precision accurate matrix interpolative decomposition approximation under a given set of criteria. Though low precision arithmetic suffers from quicker accumulation of round-off error, for many data-rich applications we nevertheless attain viable approximation accuracy, as the error incurred using low precision arithmetic is dominated by the error inherent to low-rank approximation. We then conduct several simulated numerical tests to demonstrate the efficacy of the algorithms and the corresponding error estimates. Finally, we present the application of our algorithms to a problem in model reduction for particle-laden turbulent flow.
