There have been a couple of papers for the solution of the nonsingular symmetric saddle-point problem using three-parameter iterative methods. In most of them, regions of convergence for the parameters are found, while in three of them, optimal parameters are determined, and in one of the latter, many more cases, than in all the others, are distinguished, analyzed, and studied. It turns out that two of the optimal parameters coincide making the optimal three-parameter methods be equivalent to the optimal two-parameter known ones. Our aim in this work is manifold: (i) to show that the iterative methods we present are equivalent, (ii) to slightly change some statements in one of the main papers, (iii) to complete the analysis in another one, (iv) to explain how the transition from any of the methods to the others is made, (v) to extend the iterative method to cover the singular symmetric case, and (vi) to present a number of numerical examples in support of our theory. It would be an omission not to mention that the main material which all researchers in the area have inspired from and used is based on the one of the most cited papers by Bai et al. (Numer. Math. 102:1–38, 2005).

使用三参数迭代方法解决非奇异对称鞍点问题已有两篇论文。在大多数方法中，找到了参数的收敛区域，而在其中三种方法中，确定了最佳参数，在后一种方法中，区别，分析和研究了比其他方法更多的情况。事实证明，两个最优参数是一致的，这使得最优三参数方法等同于最优已知两参数方法。我们在这项工作中的目标是多种多样的：（i）证明我们提出的迭代方法是等效的；（ii）稍微更改其中一份主要论文中的某些陈述，（iii）完成另一份论文中的分析，（iv ）说明如何从任何一种方法过渡到其他方法，（v）扩展迭代方法以涵盖奇异对称情况，并且（vi）提出许多数值示例以支持我们的理论。不用说，该地区所有研究人员启发和使用的主要材料都是基于Bai等人引用最多的论文之一。（Numer。Math。102：1-38，2005）。