In this paper, we define s-nonstationary iterative process and obtain its properties. We prove, that for any one-point iterative process without memory, there exists an s-nonstationary process of the same order, but of higher efficiency by the criteria of Traub and Ostrowski. We supply constructions of s-nonstationary processes for Newton’s, Halley’s, and Chebyshev’s methods, obtain their properties and, for some of them, also their geometric interpretation. The algorithms we present can be transformed into computer programs in a straightforward manner. Additionally, we illustrate numerical examples, as demonstrations for the methods we present.

在本文中，我们定义小号-nonstationary迭代过程，并获得其属性。我们证明，对于任何没有记忆的单点迭代过程，都会存在一个相同阶数的s非平稳过程，但是按照Traub和Ostrowski的准则，效率更高。我们为牛顿，哈雷和切比雪夫的方法提供s-非平稳过程的构造，获取它们的性质，并且对于其中的一些方法，还提供其几何解释。我们提出的算法可以直接转换为计算机程序。此外，我们还举例说明了一些数字示例，作为对我们介绍的方法的演示。