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Numerical Algorithms

Erschienen in:

14.03.2020 | Original Paper

Nonstationary vs. stationary iterative processes

verfasst von: Luba Sapir, Tamara Kogan, Ariel Sapir, Amir Sapir

Erschienen in: Numerical Algorithms | Ausgabe 2/2021

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Abstract

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.

Vorheriger Artikel Symplecticness conditions of some low order partitioned methods for non-autonomous Hamiltonian systems

Nächster Artikel Local error estimation and step size control in adaptive linear multistep methods

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Titel: Nonstationary vs. stationary iterative processes
verfasst von: Luba Sapir
Tamara Kogan
Ariel Sapir
Amir Sapir
Publikationsdatum: 14.03.2020
Verlag: Springer US
Erschienen in: Numerical Algorithms / Ausgabe 2/2021
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-020-00899-5

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