For the discrete linear system resulted from the considered steady-state space-fractional diffusion equations, we propose an improved scaled HSS (ISHSS) iteration method and discuss its convergence theory. Then, we construct a fast ISHSS (FISHSS) preconditioner to accelerate the convergence rates of the Krylov subspace iteration methods. We discuss the spectral properties of the FISHSS preconditioning matrix. Numerical experiments show the good performance of the FISHSS preconditioner.

中文翻译：

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稳态空间分数扩散方程的快速改进的HSS预调节器

对于考虑了稳态空间分形扩散方程的离散线性系统，我们提出了一种改进的比例缩放HSS（ISHSS）迭代方法并讨论了其收敛原理。然后，我们构造了一个快速ISHSS（FISHSS）预处理器，以加快Krylov子空间迭代方法的收敛速度。我们讨论了FISHSS预处理矩阵的光谱特性。数值实验表明，FISHSS预处理器具有良好的性能。