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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 10, Pages 1770–1774 (Mi zvmmf9552)  
This article is cited in 2 scientific papers (total in 2 papers)

On the quadratic convergence of the Aitken $\Delta^2$ process

V. M. Verzhbitskii, I. F. Yumanova

Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia
Full-text PDF (537 kB) Citations (2)
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Abstract: The Aitken $\Delta^2$ method for finding fixed points of scalar mappings is interpreted as a modification of the Wegstein method. Based on this approach, conditions for the quadratic convergence of this method are obtained for various situations of convergence/divergence of simple iteration. An algorithm for calculating fixed points that keeps track of these situations is presented.
Key words: scalar equation, Aitken $\Delta^2$ process, Wegstein method, quadratic convergence, algorithm.
Received: 05.04.2011
English version:
Computational Mathematics and Mathematical Physics, 2011, Volume 51, Issue 10, Pages 1659–1663
DOI: https://doi.org/10.1134/S0965542511100162
Bibliographic databases:
Document Type: Article
UDC: 519.615
Language: Russian
Citation: V. M. Verzhbitskii, I. F. Yumanova, “On the quadratic convergence of the Aitken $\Delta^2$ process”, Zh. Vychisl. Mat. Mat. Fiz., 51:10 (2011), 1770–1774; Comput. Math. Math. Phys., 51:10 (2011), 1659–1663
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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