Nonstationary iterative processes

2019/11/04 by Luba Sapir, Tamara Kogan, Sapir, Luba +5
Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical and Theoretical Analysis #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1911.01404

openalex publication_date 2019/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Optimal Order of One-Point and Multipoint Iteration

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