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arXiv · 1911.01404

Nonstationary iterative processes

Luba Sapir·Tamara Kogan·Ariel Sapir·Amir Sapir
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Abstract

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.

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Luba Sapir, Tamara Kogan, Ariel Sapir, Amir Sapir. 2019-11-04. Nonstationary iterative processes. https://arxiv.org/abs/1911.01404

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