Abstract：Sparse linear equations are the core of many large scientific computing tasks. Although parallel algorithms are providing powerful, new tools for solving sparse linear equations, existing parallel algorithms have some drawbacks such as the optimal sub-matrix being difficult to obtain and the algorithms requiring a large overhead to synchronize parallel tasks. This paper presents a parallel algorithm for sparse linear equations based on the variable correlation decomposition method. Firstly, the algorithm performs an incomplete LU decomposition on the coefficient matrix to obtain two equations for the upper and lower triangles. Then, the correlation between y and x is used to solve for the independent part of the variable in parallel from the upper and lower triangles. All the individual partial values are then added to get the final value of the variable. Since the solution does not need to wait for all the previous variables to be calculated, the partial value calculation can be performed in parallel as the calculation proceeds, which significantly reduces the algorithm execution time and improves the algorithm solution speed and parallelism. Tests show that this sparse linear equation solver is more than 50% faster than the parallel solution method in the cusparse library.
刘珊瑕, 靳松, 王文琛, 汪宇航, 王瑜. 基于变量相关性分解方法的稀疏线性方程组并行求解算法[J]. 清华大学学报（自然科学版）, 2020, 60(4): 312-320.
LIU Shanxia, JIN Song, WANG Wenchen, WANG Yuhang, WANG Yu. Parallel algorithm for solving sparse linear equations based on variable correlation decomposition. Journal of Tsinghua University(Science and Technology), 2020, 60(4): 312-320.
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