标题： 非平稳迭代过程 显示英文标题

标题： Nonstationary iterative processes

摘要： 在本文中，我们根据J. F. Traub和A. M. Ostrowski的标准，提出了高效迭代方法。我们定义{\it s非平稳迭代过程}并证明，对于任何无记忆的单点迭代过程，例如牛顿法、哈雷法、切比雪夫法，都存在一个相同阶数但效率更高的s非平稳过程。我们提供了这些方法的构造，获得了它们的性质，并且对其中一些方法还获得了它们的几何解释。我们提出的算法可以以直接的方式转换为计算机程序。这些方法通过数值例子进行了演示。 显示英文摘要

摘要： In this paper we present iterative methods of high efficiency by the criteria of J. F. Traub and A. M. Ostrowski. We define {\it s-nonstationary iterative processes} and prove that, for any one-point iterative process without memory, such as, for example, Newton's, Halley's, Chebyshev's methods, there exists an s-nonstationary process of the same order, but of higher efficiency. We supply constructions of these methods, obtain their properties and, for some of them, also their geometric interpretation. The algorithms we present can be transformed into computer programs in straight-forward manner. The methods are demonstrated by numerical examples.