正则化HSS预处理鞍点矩阵的多尺度算法

A Multiscale Algorithm for Regularizing HSS Preprocessing Saddle Point Matrix

针对鞍点求解结果收敛速度慢、CPU消耗时间较长等问题,提出一种正则化HSS预处理鞍点矩阵的多尺度算法。运用最优正则化方法确定正则参数,得到计算最优正则参数公式;通过HSS方法完成系数矩阵预处理,得到新的预处理子NHSS;为了更加具体地分析预处理后的鞍点矩阵多尺度算法特征值分布形态,择优选取预处理子参数,确保算法收敛速率。通过仿真,结果表明所提算法可以提升鞍点矩阵方程求解的收敛速率,减少计算过程的CPU占用率,具有较好的鲁棒性,在大规模线性方程运算中可进行广泛应用。

Due to slow convergence speed and high CPU utilization percentage, this article presented a multi-scale algorithm of saddle point matrix based on regularized HSS preprocessing. The optimal regularization method was used to determine the regularization parameters, and then the formula for calculating the optimal regularization parameters was obtained. Moreover, the coefficient matrix was preprocessed by the HSS method, and then a new preprocessor NHSS was obtained. In order to analyze the eigenvalue distribution of the multi-scale algorithm of the saddle point matrix after preprocessing more specifically, the preprocessing sub-parameters were selected to ensure the convergence rate of the algorithm. Simulation results show that the proposed algorithm can improve the convergence rate of solving the saddle point matrix equation, reduce CPU utilization percentage. In addition, this algorithm has good robustness, so it can be widely applied in large-scale linear equation operations.