For the discrete linear system resulting from certain steady-state space-fractional diffusion equations, we construct a lopsided scaled HSS (LSHSS) iteration method and establish its convergence theory. From the LSHSS, we obtain the corresponding matrix splitting preconditioner. By further replacing the involved Toeplitz matrix with certain circulant matrix, we construct a fast LSHSS (FLSHSS) preconditioner in order to accelerate the convergence rates of the Krylov subspace iteration methods. Theoretical analyses and numerical experiments show good performance of the FLSHSS preconditioning.

中文翻译：

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稳态空间分数扩散方程的不平衡缩放 HSS 预处理器

对于由某些稳态空间分数扩散方程产生的离散线性系统，我们构建了一种不平衡缩放HSS（LSHSS）迭代方法并建立了其收敛理论。从LSHSS，我们得到相应的矩阵分裂预处理器。通过进一步用某个循环矩阵替换所涉及的 Toeplitz 矩阵，我们构造了一个快速 LSHSS（FLSHSS）预处理器，以加快 Krylov 子空间迭代方法的收敛速度。理论分析和数值实验表明 FLSHSS 预处理具有良好的性能。