线性代数
计算机科学
稀疏矩阵
乘法(音乐)
数值线性代数
矩阵乘法
并行计算
张量代数
瓶颈
稀疏逼近
基质(化学分析)
理论计算机科学
线性系统
域代数上的
算法
代数表示
数学
除法代数
数学分析
物理
几何学
量子力学
组合数学
纯数学
嵌入式系统
量子
高斯分布
材料科学
复合材料
作者
Xiaoxue Li,Chuanghui Yin,Tao Zhou,Xueqi Li,Yuedan Chen,Kenli Li
摘要
Sparse linear algebra includes the fundamental and important operations in various large-scale scientific computing and real-world applications. There exists performance bottleneck for sparse linear algebra since it mainly contains the memory-bound computations with low arithmetic intensity. How to improve its performance has increasingly become a focus of research efforts. Using parallel computing techniques to accelerate sparse linear algebra is currently the most popular method, while facing various challenges, e.g., large-scale data brings difficulties in storage, and the sparsity of data leads to irregular memory accesses and parallel load imbalance. Therefore, this article provides a comprehensive overview on acceleration of sparse linear algebra operations using parallel computing platforms, where we focus on four main classifications: sparse matrix-vector multiplication (SpMV), sparse matrix-sparse vector multiplication (SpMSpV), sparse general matrix-matrix multiplication (SpGEMM), and sparse tensor algebra. The takeaways from this article include the following: understanding the challenges of accelerating linear sparse algebra on various hardware platforms; understanding how structured data sparsity can improve storage efficiency; understanding how to optimize parallel load balance; understanding how to improve the efficiency of memory accesses; understanding how do the adaptive frameworks automatically select the optimal algorithms; and understanding recent design trends for acceleration of parallel sparse linear algebra.
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