Nonstationary vs. stationary iterative processes

Autor:	Tamara Kogan, Ariel Sapir, Luba Sapir, Amir Sapir
Rok vydání:	2020
Předmět:	Iterative and incremental development Applied Mathematics Numerical analysis Existential quantification Theory of computation Process (computing) Applied mathematics Order (ring theory) Chebyshev filter Interpretation (model theory) Mathematics
Zdroj:	Numerical Algorithms. 86:515-535
ISSN:	1572-9265 1017-1398
DOI:	10.1007/s11075-020-00899-5
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::178c21e94867cc6e04fa9226082c25b4 https://doi.org/10.1007/s11075-020-00899-5 Zobrazit plný text záznamu Full text from SpringerLink