For solving a class of block two-by-two real linear system, a new single-step iteration method based on triangular splitting scheme is proposed in this paper. Then the convergence properties of this method are carefully investigated. In addition, we determine its optimal iteration parameters and give the corresponding optimal convergence factor. It is worth mentioning that the SSTS iteration method is robust and superior to SBTS and PSBTS iteration methods under suitable conditions. Finally, some numerical experiments are carried out to validate the theoretical results and evaluate this new method.

翻译：为了解决一组区块二比二实际线性系统,本文件提出了基于三角分裂办法的新的单步迭代方法。然后仔细调查这一方法的趋同特性。此外,我们决定其最佳迭代参数,并给出相应的最佳趋同系数。值得一提的是,SSTS迭代方法在适当条件下既健全又优于SBTS和PSBTS迭代方法。最后,进行了一些数字实验,以验证理论结果和评估这一新方法。