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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 12, Pages 1951–1969
DOI: https://doi.org/10.7868/S0044466913120065 (Mi zvmmf9954) 		 
This article is cited in 6 scientific papers (total in 6 papers)

$p$th-order approximation of the solution set of nonlinear equations

Yu. G. Evtushenkoa, A. A. Tret'yakovbc

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b University of Podlasie, 3 Maja 54, 08-110, Siedlce, Poland
c System Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland
Full-text PDF (336 kB) Citations (6)
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DOI: https://doi.org/10.7868/S0044466913120065
Abstract: Given a system of nonlinear equations, a formula is derived for the family of its approximate solutions of up to the pth order of smallness. A formula approximating an implicit function up to the third order of smallness is presented. Iterative methods converging with the $p$th order are constructed for solving systems of nonlinear equations. These results are extended to the degenerate case. Examples of applying the results are given.
Key words: nonlinear equations, $p$th-order approximations, generalized implicit function theorem, iterative method, degenerate case.
Received: 30.04.2013
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 12, Pages 1763–1780
DOI: https://doi.org/10.1134/S0965542513120051
Bibliographic databases:
Document Type: Article
UDC: 519.642.8
Language: Russian
Citation: Yu. G. Evtushenko, A. A. Tret'yakov, “$p$th-order approximation of the solution set of nonlinear equations”, Zh. Vychisl. Mat. Mat. Fiz., 53:12 (2013), 1951–1969; Comput. Math. Math. Phys., 53:12 (2013), 1763–1780
Citation in format AMSBIB
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    • This publication is cited in the following 6 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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