We propose an improved version of the Hermitian/skew-Hermitian splitting (HSS) iterative method, which we call HSS(0), to solve non-Hermitian linear systems with a positive definite Hermitian part. The improvement is based on solving the Hermitian half iteration without a shift, and applying a shift only for the skew-Hermitian solve. An optimal parameter is derived analytically, and a corresponding upper bound on the convergence speed is obtained. Using a combination of analytical proofs and numerical validations, we show that HSS(0) yields a dramatically faster convergence speed than standard HSS. Furthermore, HSS(0) is much less sensitive to the choice of the parameter. Numerical experiments on a convection-diffusion model problem in two and three dimensions illustrate the high efficiency of HSS(0).

翻译：我们建议改进Hermitian/skew-Hermitian(HSS)迭代法(HSS)的版本,我们称之为HSS(0),用一个肯定的Hermitian部分解决非Hermitian线性系统。改进的基础是解决Hermitian半迭代,不作任何改变,只对 skew-Hermitian 溶液进行转换。一个最佳参数是通过分析推导得出,并获得对趋同速度的相应上限。使用分析证据和数字验证的结合,我们表明HSS(0)的趋同速度比标准HSS快得多。此外,HSS(0)对参数的选择敏感度要低得多。两个和三个层面的关于对等集成模型问题的数值实验显示了HSS(0)的高度效率。